Question

If you vertically compress the absolute value parent function, f(x) = [ 41, by a

Answer 1

Answer:

$g(x) = \frac{1}{5} |x|$

Step-by-step explanation:

Given

$f(x) = |x|$

Vertically compressed

Compression Factor = 5

Required

Find the equation of the new function;

Let the new function be represented by g(x)

Let c represented the compression factor;

such that c = 5

When a function f(x) is vertically compressed by factor c, the new function becomes

$f(\frac{1}{c}x)$

From properties of functions;

$f(\frac{1}{c}x) = \frac{1}{c} *f(x)$

This implies that

$g(x) = f(\frac{1}{c}x) = \frac{1}{c} *f(x)$

$g(x) = \frac{1}{c} *f(x)$

Recall that $f(x) = |x|$ and c = 5

$g(x) = \frac{1}{5} * |x|$

$g(x) = \frac{1}{5} |x|$

Hence, the new function is $g(x) = \frac{1}{5} |x|$