Chapter 4: Q. 107 (page 195)

$G (x) = {(x + 3)}^{2} (x - 2)$
(a) Identify the $x$ -intercept of the graph of $G$
(b) What are the $x$ -intercepts of the graph of $y = G (x + 3)$

Short Answer

Expert verified

(a) x-intercepts of $G (x)$ are $- 3, 2$

(b) x-intercepts of $G (x + 3)$ are $- 1, - 6$

Step by step solution

Part (a) Step 1. Solve for x

Set $y = 0$ in the given function and solve for $x$

localid="1646133381864" ${(x + 3)}^{2} (x - 2) = 0 (x + 3) = 0; (x - 2) = 0 x = - 3; x = 2$

Thus, the x-intercepts are: $x = - 3, 2$

Part (b) Step 1. Substitute x with x+3

We have,

$G (x + 3) = {(x + 3 + 3)}^{2} (x + 3 - 2) G (x + 3) = {(x + 6)}^{2} (x + 1)$

Part (b) Step 2. Find the x-intercept of G(x+3)

${(x + 6)}^{2} (x + 1) = 0 (x + 6) = 0; (x + 1) = 0 x = - 6; x = - 1$

So, the x-intercepts are $- 6, - 1$

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$G (x) = {(x + 3)}^{2} (x - 2)$
(a) Identify the $x$ -intercept of the graph of $G$
(b) What are the $x$ -intercepts of the graph of $y = G (x + 3)$

Short Answer

Step by step solution

Part (a) Step 1. Solve for x

Part (b) Step 1. Substitute x with x+3

Part (b) Step 2. Find the x-intercept of G(x+3)

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G(x)=(x+3)2(x-2)(a) Identify the x-intercept of the graph of G(b) What are the x-intercepts of the graph ofy=G(x+3)

Short Answer

Step by step solution

Part (a) Step 1. Solve for x

Part (b) Step 1. Substitute x with x+3

Part (b) Step 2. Find the x-intercept of G(x+3)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

$G (x) = {(x + 3)}^{2} (x - 2)$
(a) Identify the $x$ -intercept of the graph of $G$
(b) What are the $x$ -intercepts of the graph of $y = G (x + 3)$