Graph of x 3 3x Solution. Log In Sign Up. Let f(x) = 2x^3+3x^2-36x, Sketch the graph of f(x). $$ \lim_{x \to \infty} \left( x^3-3x^2+3x+2 \right) = \lim_{x \to \infty} x^3 = \color{blue}{ \infty } $$ The graph ends in the upper-right corner. Reorder and . Tap for more steps Step 3. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step Aug 30, 2023 · The y-intercept is the point where the graph of a function crosses the y-axis. Slope: Question: for what values of x does the graph of f(x)=x3+3x2+x+3 have a horizontal tangent? for what values of x does the graph of f(x)=x 3 +3x 2 +x+3 have a horizontal tangent? There are 3 steps to solve this one. STEP 4:Find Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The slope-intercept form is , where is the slope and is the y-intercept. Expression 1: negative 2 "x" equals 2 "y" minus 4. You get now the variations of f : - f is decreasing on [0,2] - f is creasing on [-oo, 0] and Free online graphing calculator - graph functions, conics, and inequalities interactively 12 hours ago · Click here 👆 to get an answer to your question ️Find the limit x -1 f(x) by using the graph of the following function (f(x) = x2 + 1 x 1 3x + 2 -1 x 1 2 - x x 1 ) Study tools. Thus, f(x) becomes -3 (|3x| + 4). Related Symbolab blog posts. 6 which is roughly the solution to Click here 👆 to get an answer to your question ️ Which translation shifts the graph of f(x)=3x+3 onto g(x)=3x-3 ？ 3 units up 6 units down 3 units down 6 units Which translation shifts the graph of f(x)=3x+3 onto g(x)=3x-3 ？ 3 units up 6 units down 3 units down 6 units up. The final answer is . The absolute value can be graphed using the points around the vertex. You can click-and-drag to move the graph around. Use a graph calculator to graph f(x) = 3x^2 - 8/x^2 - 4. 3 Draw the graph of Solve your math problems using our free math solver with step-by-step solutions. powered by Correct Answer: Option B Explanation If the graph of y = x 3 - 3x + 1 is plotted,the graph crosses the x-axis in the ranges -2 x -1 and 0 x 1 Investigate the behaviour of the function y = x 3 - 3x + 2 and construct its graph. Step 2. If you just click-and-release (without moving), then the spot you clicked on will be the new center. Math can be an intimidating subject. The end behavior of a polynomial function is determined by the leading term, which is the term with the highest Free online graphing calculator - graph functions, conics, and inequalities interactively Dec 10, 2017 · The value of x for the graphs will be calculated as below:-f(x) = 3 x 3 -2x. gx=fx+8 4. Therefore, the new function g(x) following the transformations will be g(x) = 3 |3x| + 12. Asked in United Kingdom. To graph the function f (x) = x 3 − 3 x 2, we need to analyze its key features such as intercepts, critical points, and behavior at the endpoints. Log InorSign Up. We have to choose 2 points on our equation : For Explore math with our beautiful, free online graphing calculator. Apr 12, 2018 · A graph that has the same end behavior as the graph of f(x) = -3x³ - x² + 1 is the graph of g(x) = -x³ (option 4). The points would be (i)x=3, y=3^3 -3*3=18, that is (3,18) and (ii)x= -3, y= (-3)^3 -3(-3) = -18 The graph of the equation 3 x 2 + 4 x + 5 = 0 intersects the x-axis at point(s). Slope of the graph at any point is dy/dx = 3x^2 -3. -1± sqrt(5) D. Zero of a function: To find the zero of a function f(x), we need to find the value of f(0). STEP 4:Find the turning points. What are the other zeros of the function? desmos North Carolina Grade 8, Math 1, and above Version + 1 2 2885 A. Simplify the result. The entry is an x. -2 and 2 B. On a coordinate plane, a line decreases through What is the solution of x^4-3x^3+x^2+3x-2 0 ? May 28, 2017 · relative maximum: (-1, 6) relative minimum: (3, -26) Given: f(x) = x^3 - 3x^2 - 9x + 1 Find the critical numbers by finding the first derivative and setting it equal to zero: f'(x) = 3x^2 -6x - 9 = 0 Factor: (3x + 3 )(x -3) = 0 Critical numbers: x = -1, " "x = 3 Use the second derivative test to find out if these critical numbers are relative maximums or relative minimums: f''(x) = 6x - 6 f Given expression x 3 - 3x 2 - x + 3. If you applied the formula correctly, all the points will miraculously line up in a straight line! graph{y=3x+3 [-10, 10, -5, 5]} By On the grid, draw the graph of y=3x-1 for values of x from −2 to 3 -7. Step 1 Derive: y'(x)=3x^2-6x+1 Step2: Evaluate: y'(2)=12-12+1=1 Step3: The graph of the function f(x) = 2x^4 - x^3 + 5x^2 - 3x - 9 will behave like the graph of for large values of |x|. Given: fx=2x3-5x2-4x+3 1. Jan 18, 2019 · The function f (x) = x 3 − 3 x 2 − 4 x has the following characteristics: Factors: x (x + 1) (x − 4) Zeros/roots: x=0, x=-1, amd x=4; Positive leading coefficient; Graph starts down and curves up through -1 on the x-axis Find Where Increasing/Decreasing y=x^3. Start by simplifying the right side while having in mind your operation priorities. Expert Verified Solution Super Gauth AI. 2. This means that x = -1 is a solution, and x = 2 is also a solution (of multiplicity 2). In this case, the vertex for is . 34729,x\approx-1. Feb 3, 2015 · I would find the derivative of your function, y'(x), evaluate the derivative at the point of interest (x=2) and use it as the slope of the line through (2,-2). To get graph, take sample points for (x, y) and plot them on X-Y axis. Graph the equation in order to determine the intervals over which it is increasing or decreasing. Solve for . 3x = 3 ( 3 ) -2x. Describe how the graph can be obtained from the graph of a basic exponential function. Use a graphing utility to graph the equation 3x^2 + 2xy + y^2 - 10 = 0. Asked in Sketch the graph of f(x) = x^3 - 3x^2 - 9x. 免费使用Desmos精美的在线图形计算器来探索数学奥妙。功能包含绘制函数图形和散点图，视化代数方程式、新增滑块，动画图表等。快来使用我们既精美又免费的在线图形计算器，一同探 Graph your problem using the following steps: Type in your equation like y=2x+1 (If you have a second equation use a semicolon like y=2x+1 ; y=x+3) Linear Approximation: Use Differentials to estimate \sqrt {3. Interactive, free online calculator from GeoGebra: graph functions, plot data, drag sliders, create triangles, circles and much more! Assessment '1 ALL 2024 / 3 of 30 The graph of the function m(x)=x^3+3x^2-2x-4 has a zero at -1. Label all maximum(s), minimum(s), inflection point(s), Graph y=x^3. What is graph? The link between lines and points is described by a graph, which is a mathematical description of a network. Question: Sketch the graph of f(x) = 3x - 2. Expert Verified Solution Super Gauth Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. hx=fx-7 3. To reset the zoom to the original click on f(x) = (x^2 - 3x + 9)/(x - 3) = (x^2 - 3x)/(x - 3) + 9/(x - 3) = (x(x - 3))/(x - 3) + 9/(x - 3) = x + 9/(x - 3) So you actually wanna sketch f(x) = x + 9/(x - 3) Domain: The domain of this function is all Real x except 3 because 9/(x - 3) would become Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. The equation of the horizontal asymptote is . When the function's values are equal to zero, the values of x are the function's zeros. we need to find the first derivative of $ p(x) $: $$ p^{\prime} (x) = 3x^2+2x $$ The x coordinate of the turning points are located at the zeros of Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. 1M people helped Find Where Increasing/Decreasing y=x^3. Reflecting across the x-axis implies changing the sign of the output. Graph the parabola using its properties and the selected points. y = \dfrac{2}{3}x + 4; Sketch the graph of f(x) = 6x^3/(x^3 + 8) Sketch a graph of f(x) = (1/4)^x. Graph y=3x-3. Graph the following quadratic equation and state their nature of solution (2x – 3) (x + 2) = 0. The next Sketch the graph 3x - 6y = 12; Sketch the graph of y = 2 - x^3. Sketch the graph of f(x) f(x)=\frac{\cos(x)}{1+\sin(x)} Sketch the graph. 1. My suggestion to graphing y=3x+3 is to find a whole bunch of values of x and y values, plotting them onto graph paper and then drawing a straight line through them. 9, 172. This online calculator computes and graphs the roots (x-intercepts), signs, local maxima and minima, increasing and decreasing intervals, points of Inflection and concave up-and-down intervals. AI Homework Helper; Math Solver; Math AI; AI Tutor; Ask AI Questions; AI Answer Generator; Code Generator; Subjects. If , then the x-axis, , is the horizontal asymptote. Plot only three points per line. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Find the point at . Find where the expression is undefined. 53208,x\approx 1. 183, -1. Explore math with our beautiful, free online graphing calculator. Asked in United States. Consider the rational function where is the degree of the numerator and is the degree of the denominator. Draw the graph of y = x 2 – 5x – 6 and hence solve x 2 – 5x – 14 = 0. Graph f(x)=3-x^2. The slope of the line is the value of , and the y-intercept is the value of . Create a table of values for the graph of 3x+2y=12 where the values of x are from −1 to 3. If the tangent line at some point, is parallel to y= 24x +15, then at that particular point, slope would be 3x^2-3 = 24 On solving this, x = +- 3 Thus there are two such points with x-coordinate =+-3. Explore math with our beautiful, free online graphing calculator. Let y = x 3 - 3x 2 - x + 3. SOLUTION: draw the graph of 3x+y=3. 2. To find the coordinate of the vertex, set the inside of the absolute value equal to . Find the values of and using the form . Solvers Solvers. 87938 Nov 1, 2021 · Starting from the left, the first zero occurs at \(x=−3\). Free functions turning points calculator - find functions turning points step-by-step Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Tap for more steps Step 2. There are 2 steps to solve this one. Graph each side of the equation. 1、 gx=fx+12 2. -1 and 4 C. we know that. Graph y=sin(1/3x) Step 1. f(x) = 2x^3 + 3x^2 - 1; The values of x for which the graph of f(x)=x 3 +3x 2 +x+3 has a horizontal tangent are -0. Clearly indicate all intercepts with the axes and coordinates of turning points. The solutions to the equation x^3-3x-1=0 are x\approx-0. For any , vertical asymptotes occur at , where is an integer. Step-by-step solution and graphs included! Switch light/dark mode Integral Calculator Calculate integrals online — with steps and graphing! Also check the Derivative Calculator! Calculadora de Integrales en español Integralrechner Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! Name _enVision Algebra 1 Rávvarrealisa rom 3-3 Additional Practice Transforming Linear Functions Suppose fx=3x+5 Describe how the graph of each function compares to f. Convert to decimal. Tap for more steps Step 1. Each new topic we learn has symbols and problems we have never seen. A given circle x 2 + y 2 + 2 g x + 2 f y + c = 0 touches the x-axis and intersects the y-axis at 2 points. If a polynomial function has integer coefficients, then every rational zero will have the form where is a factor of the constant and is a factor of the leading coefficient. 1 Neatly draw the graph of f on the graph paper given in ANNEXURE A. Draw the graph of y = x 2 + 3x + 2 and use it to solve x 2 + 2x + 1 = 0. Graph f(x)=3x-1. How many values of x are possible for y = 0. Horizontal Asymptote: Step 2 Aug 29, 2016 · #f(x)=x ^3+3x^2+7x-1# The gradient function is the first derivative #f'(x)=3x^2+6x+7# So the gradient when X=-1 is 3-6+7=4 The gradient of the normal , perpendicular, to the tangent is #-1/4#. Sketch the graph of y = sec x / 2. 2 Determine the first derivative of f and call it g. Amplitude: Step 3. Subtract from both sides of the equation. View Solution. The table of values for the graph of 3x + 2y = 12, where x ranges from -1 to 3, is shown above. Step by Step Solution: Step 1 Solve your math problems using our free math solver with step-by-step solutions. Jul 4, 2021 · The solution of the graph function y=x³+x²-6x are -3 , 0 and 2 . Sep 2, 2024 · The graph of f(x) = x^3 - 3x^2 + 4 passes through x = -1, and bounces off x = 2. 3x = 9 - 2x. graph x^{4}-3x^{3} en. AI may present inaccurate or offensive content that does not represent Symbolab's views. Use the graph to answer the question. Replace the variable with in the expression. Graph the line using the slope and the y-intercept, or the points. we have . Step 2 The graph of f(x)=x^4-3x^3+x^2+3x-2 is shown. Find the properties of the given parabola. Q5. Sketch the graph of f(x) = 3x - 2. 100% (17 rated) Answer. Misc 2 Sketch the graph of y = |𝑥+3| and evaluate ∫_(−6)^0 〖│𝑥+3│ 𝑑𝑥〗 Let’s Draw the graph y = |𝒙+𝟑| y = |𝑥+3 Solve by Graphing x^3-3x^2-13x=-15. Sketch the graph of f(x) = 3x^2 - x^3. gx=4fx 6、 gx=f5x What value of k transforms the graph of fx=0. If you are not sure about this draw a line with gradient 4 on squared paper and draw the perpendicular. To start with, we need to Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. 5x = 9. Exponential functions have a horizontal asymptote. Draw the graph of the function y = a x. The graph touches the \(x\)-axis, so the multiplicity of the zero must be even. 4. Draw the graph of y = 2x 2 – 3x – 5 and hence solve 2x 2 – 4x – 6 = 0 Graph f(x)=3^x. 4 days ago · x 2 – 6x + 9 = 0. 6, -85. Dec 3, 2020 · The other zeros of function m(x) = x^3 + 3x^2 - 2x - 4 are x = 2, x = -2. Set the inside of the tangent function, , for equal to to find where the vertical asymptote occurs for . Label all maximum(s), minimum(s), inflection point(s), Interactive, free online calculator from GeoGebra: graph functions, plot data, drag sliders, create triangles, circles and much more! Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. line\:(1,\:2),\:(3,\:1) f(x)=x^3 ; prove\:\tan^2(x)-\sin^2(x)=\tan^2(x)\sin^2(x) \frac{d}{dx}(\frac{3x+9}{2-x}) (\sin^2(\theta))' \sin(120) \lim _{x\to 0}(x\ln (x)) \int e^x\cos (x)dx Free graphing calculator instantly graphs your math problems. 1± 2sqrt(3) Asked in United States. Find the amplitude . 816 Explore math program Math worksheets and visual curriculum Nov 22, 2022 · The graph of the polynomial f(x) is added as an attachment. Take 2 cm=1 unit on both the axes, (i) Draw the graphs of x+y+3=0 and 3x-2y+4=0. − 2 x = 2 y − 4. . Show transcribed image text. Step 1: Be familiar with the graph of the basic cubic function {eq}y=x^3 {/eq}, as the graph of {eq}y=ax^3 {/eq}, where {eq}a {/eq} is a real Free tangent line calculator - find the equation of the tangent line given a point or the intercept step-by-step Free online graphing calculator to graph functions, conics, and inequalities interactively. Find the absolute value vertex. graph of x3 - 3x - 7. 99} and find a point on the Graph of y=x^3-3x Question: What are all values of k for which the graph y = x^3 - 3x^2 + k will have three distinct x - intercepts? Show transcribed image text. On functions, one-to-one activities, many-to-one functions, within functions, and also on functions are the four principal types of functions that seem to be available. Factor by grouping to find zeros: \displaystyle{2},-{2},-{3} Explanation: Notice that the ratio between the first and second terms is the same as that between the third and fourth terms. x 3 − 3 x − 7. 6]} FIrst determine the interval of definition, then the behavior of first and second derivatives and the behavior of the function as xapproaches +-oo 1) The function is a polynomial and is defined for x in (-oo,+oo) 2) The highest monomial is of odd order so: lim_(x->-oo) y(x) = -oo lim_(x->+oo) y(x) = +oo Also (y(x))/x does Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Step 3. In the given function, f(x) = 3x – 3, the y-intercept represents the value of f(x) when x = 0. Increasing on: Step 2 Sketch the graph 3x - 6y = 12; Sketch the graph of y = 2 - x^3. 3x + y = 3 Subtract 3x from both sides . Increasing on: Step 2 This online calculator computes and graphs the roots (x-intercepts), signs, local maxima and minima, increasing and decreasing intervals, points of Inflection and concave up-and-down intervals. we need to find the first derivative of $ p(x) $: $$ p^{\prime} (x) = 3x^2-4x-24 $$ The x coordinate of the turning points are located at the zeros Solve your math problems using our free math solver with step-by-step solutions. How to plot the graph of the polynomial? From the question, the equation of the polynomial is given as. Here is the graph of 3x-y=2 for values of x from 0 to 2 drawing a second graph on the grid. Factor using the rational roots test. given. Show transcribed image text There’s just one step to solve this. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. -3 (|3x| + 4) becomes 3 (|3x| + 4). In this problem the apparent zeros are Graph k(x)=-3x+3. To find the x-intercepts solve, the equation $ \color{blue}{ x^3-3x-2 = 0 } $ The solutions of this equation are: $$ \begin{matrix}x_1 = 2 & x_2 Graph 3x-2y=12. A cubic is a polynomial which has an x 3 term as the highest power of x. Linear Approximation: Use Differentials to estimate \sqrt {3. How to Graph a Cubic Function of the Form Y = Ax^3. Feb 15, 2023 · (x). 6, 73. To have three distinct x-intercepts for the equation y = x 3 Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Math; Business; Explore math with our beautiful, free online graphing calculator. Find the period of . f(x) = x^3 + 3x^2 – 4x – 12. Direction: Opens Nov 29, 2016 · graph{x^3-3x^2-9x+5 [-145. In order to know where the graph Jan 10, 2025 · 2x−3; cos(x^2) (x−3)(x+3) Zooming and Re-centering. Draw the graph of the equation, 2x - 3y = 5. In these we can be able to get the value for the Y intercept Graph y=|3x| Step 1. Explanation. May 31, 2023 · Solution For Correct graph of 3x+3y+1=0 is : ANCET 1995 CBSE PMT 2000 1 2 0 Whach of the following describes the motion comectly There is not enough date for generalization Consider the acceleration, velocity and Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. 3x = 3 x 3 -2x. Graph f(x)=3x-3. {x \to \infty} \left( x^3+3x^2+x \right) = \lim_{x \to \infty} x^3 = \color{blue}{ \infty } $$ The graph ends in the upper-right corner. 99} and find a point on the Graph of y=x^3-3x To find the x-intercepts solve, the equation $ \color{blue}{ x^3-3x-2 = 0 } $ The solutions of this equation are: $$ \begin{matrix}x_1 = 2 & x_2 = -1 & x_3 = -1 \end{matrix} $$ Feb 5, 2024 · So plotting the graphs of y=x^3-3x+2 and y=-x^3-2 should give a solution to equation 2 And it does. 5x+3 into graph g? Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Answered by Blitztiger • 679 answers • 4. Graph the following and find the roots. 3. From your graph, find (i) the value of y when x = 4 and (ii) the value of x when y = 3. Question: Sketch the graph of the function f(x) = x^3 - 3x^2 -4x + 12 on the given grid. Rewrite the equation in vertex form. To determine the turning point, we need to find the first derivative of $ p(x) $: $$ p^{\prime} (x) = 3x^2-6x+3 $$ The x coordinate of the turning point is located at Dec 8, 2017 · (3,18) and (-3,-18) You are right. What is a cubic graph? A cubic graph is a graphical representation of a cubic function. Use the slope-intercept form to find the slope and y-intercept. 3. If , then the horizontal asymptote is the line. Algebra -> Graphs-> SOLUTION: draw the graph of 3x+y=3 Log On Algebra: Graphs, graphing equations and inequalities Section. k out an approximate solution to the ultaneous equations 3x-y=2 and 2x+y=4 x= y= Point-to-Point Straight Line Shape Remove line. Find the asymptotes. There are 3 steps to solve this one. Slope: y-intercept: Step 6 Graph y=tan(3x) Step 1. Practice, practice, practice. 1. Carefully label the x-intercept(s) and y-intercept AND try to get your values approximately correct. Sketch the graph of h(x) = 1/x+4 + 2; Sketch the graph of f(x) = x1/3 + (x Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Save Copy. Graph y=3x. We want to draw y=-3x-3 Your equation is a linear equation because you can find 2 integers a and b such as : y = a*x+b (Here a=-3 and b=-3) The representative curve of a linear equation is a straight line! As you know, we need only 2 points to draw a straight line. Sketch the graph of the parabola. Now simplify the left Factor x^3-3x^2+3x-1. When a > 1. Raise to the power of . These graphs Apr 10, 2018 · For example, y=6 when x=1 (because 6=3*3+3). Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more. Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift. These two graphs intersect at x=-1. Graph (x^3-9x)/(3x^2-6x-9) Step 1. Expert Verified Solution Super Gauth AI Jun 5, 2023 · Stretching by a factor of 3 implies multiplication of the output by 3. Use the basic period for , , to find the vertical asymptotes for . The unknowing Chat with Symbo. Rewrite the function as an equation. In the following equation, identify the x-intercepts of the graph y = 3x^2 + 19x - 40? Use a graphing utility to graph the equation 3x^2 + 2xy + y^2 - 10 = 0. Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. In order to find the nature of the graph, we need to plot the graph. The graph of this transformed function would Dec 16, 2024 · Transcript. The period of the function can be calculated using . Solve your math problems using our free math solver with step-by-step solutions. f(x) = 3x^2 + 6x - 12; Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Step 1. A graph is made up of certain points Click here 👆 to get an answer to your question ️ 3 (a) Complete the table of values for y=x^3-3x-1 (b) On the grid, draw the graph of y=x^3-3x-1 for -2≤slant Interactive, free online graphing calculator from GeoGebra: graph functions, plot data, drag sliders, and much more! Click here 👆 to get an answer to your question ️ 3 (a) Complete the table of values for y=x^3-3x-1 (b) On the grid, draw the graph of y=x^3-3x-1 for -2≤slant Jul 6, 2015 · The blue line on the graph. hx=fx-14 5. Graphing A System of Linear Equations. Divide each term in by and simplify. The solution is the x-value of the point of intersection. The zero of −3 has multiplicity 2. For what values of x does the graph of f ( x ) = 2x^3 + 3x^2 −12x − 4 have a horizontal tangent line? Answer(separate by commas): There’s just one step to solve this. Feb 24, 2015 · Calculate derivative : f'(x) = 3 x^2 - 6 x = 3x (x-2) So you can study the sign of f'(x) : f'(x) < 0 iff x in ]0,2[ f'(x) > 0 iff x in ]-oo, 0[ cup ]2,+oo[. To find the y-intercept, we substitute x = 0 into the function and solve for f(x): f(0) = 3(0) - 3 = -3. Use graph paper for this question. sxbt oen gupz sipon ztm lcsw egctpn bcuw fyfgr kmtkex