Question

If f\left(x\right)=\mid x\midf ( x ) =∣ x ∣, then what is the new function g\left(x\right)g ( x ) when f\left(x\right)f ( x ) is translated 3 units down, followed by a vertical stretch of 2? Group of answer choices

Answer 1

Answer:

$g(x) = 2 (|x| - 3)$

Step-by-step explanation:

Given

$f\left(x\right)=\mid x\mid$

Translation = 3 units down

Vertical stretch of 2 to give g(x)

Required

$g\left(x\right)$

3 units down translation

A function is translated down as follows:

$h(x) = f(x) - k$

Where k is the number of units.

So:

$h(x) = f(x) - k$

$h(x) = |x| - 3$

Vertical stretch of 2

A function is vertically stretched as follows;

$g(x) = ah(x)$

Where a is the units stretched.

In this case:

$a = 2$

So:

$g(x) = ah(x)$

$g(x) = 2 * (|x| - 3)$

$g(x) = 2 (|x| - 3)$