Chapter 4: Q. 108 (page 195)

$h (x) = (x + 2) {(x - 4)}^{3}$
(a) Identify the x-intercepts of the graph of h.
(b) What are the x-intercepts of the graph of $y = h (x - 2)$ ?

Short Answer

Expert verified

(a) x-intercepts of $h (x)$ are $- 2, 4$

(b) x-intercepts of $h (x - 2)$ are $0, 6$

Step by step solution

Part (a) Step 1. Solve for x

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

$(x + 2) {(x - 4)}^{3} = 0 x + 2 = 0; x - 4 = 0 x = - 2; x = 4$

So, the x-intercepts are $- 2, 4$

Part (b) Step 1. Substitute x with x-2

$h (x - 2) = (x - 2 + 2) {(x - 2 - 4)}^{3} h (x - 2) = x {(x - 6)}^{3}$ We have,

Part (b) Step 2. Find the x-intercepts of h(x-2)

$x {(x - 6)}^{3} = 0 x = 0; x - 6 = 0 x = 0; x = 6$

So, the x-intercepts of $h (x - 2)$ is $0, 6$

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$h (x) = (x + 2) {(x - 4)}^{3}$
(a) Identify the x-intercepts of the graph of h.
(b) What are the x-intercepts of the graph of $y = h (x - 2)$ ?

Short Answer

Step by step solution

Part (a) Step 1. Solve for x

Part (b) Step 1. Substitute x with x-2

Part (b) Step 2. Find the x-intercepts of h(x-2)

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h(x)=(x+2)(x-4)3(a) Identify the x-intercepts of the graph of h.(b) What are the x-intercepts of the graph of y=h(x-2)?

Short Answer

Step by step solution

Part (a) Step 1. Solve for x

Part (b) Step 1. Substitute x with x-2

Part (b) Step 2. Find the x-intercepts of h(x-2)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Logic and Functions

Applied Mathematics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

$h (x) = (x + 2) {(x - 4)}^{3}$
(a) Identify the x-intercepts of the graph of h.
(b) What are the x-intercepts of the graph of $y = h (x - 2)$ ?