3. Sketch a comprehensive graph of ƒ(x) = 2x(x + 2)².

Answered: 3. Sketch a comprehensive graph of f(x)…

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

3. Sketch a comprehensive graph of ƒ(x) = 2x(x + 2)².

Expert Solution

Step 1

We have given to sketch the graph of the function

$f (x) =$ $2 x {(x + 2)}^{2}$

To get x-intercept of the function

Put $f (x) = 0$

$2 x {(x + 2)}^{2}$ $= 0$

$x = 0$ or ${(x + 2)}^{2} = 0$

$x = 0$ or $x = - 2, - 2$

x=0 (multiplicity 1)

$x = - 2$ (multiplicity 2)

We get zeros of the function

$x = - 2, 0$

To get y- intercept put x=0

$f (0) =$ $0$

Put x=1

$f (1) =$ $2 {(1 + 2)}^{2}$ $= 2 {(3)}^{2}$ $= 18$

Put x=-1

$f (- 1) =$ $2 (- 1) {(- 1 + 2)}^{2}$ $= - 2$

When $x \to \infty$ , f(x) $\to \infty$

When $x \to - \infty$ , $f (x) \to - \infty$

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3. Sketch a comprehensive graph of f(x) = 2x(x + 2)².