Question

Look at the picture for the question.

Answer 1

Answer:

$g(x) = \sqrt{\frac{1}{4}x +4}$

Step-by-step explanation:

Given

$f(x) = \sqrt{x + 2$

Transformations:

1. Horizontal shrink by 1/4

2. Translation 2 units right

Required

Determine the new function

1. Horizontal shrink by 1/4

This implies that:

For:

$f(x) = \sqrt{x + 2$

After shrinking, the function is:

$f'(\frac{1}{4}x) = \sqrt{\frac{1}{4}x + 2}$

2. Translation 2 units right

For:

$f'(\frac{1}{4}x) = \sqrt{\frac{1}{4}x + 2}$

The right translation is given by:

$g(x) = f(x + b)$

Where b is the number of units translated.

So:

$g(x) = f"(\frac{1}{4}x+2) = \sqrt{\frac{1}{4}x +2+ 2}$

$g(x) = f"(\frac{1}{4}x+2) = \sqrt{\frac{1}{4}x +4}$

Hence:

$g(x) = \sqrt{\frac{1}{4}x +4}$