Question

Translate ƒ(x) = |x| so that it's translated up by 5 units and vertically stretched by a factor of 3. What's the new function g(x)? Question 20 options: A) g(x) = |3x| + 5 B) g(x) = |3x| +–5 C) g(x) = 3|x| +–5 D) g(x) = 3|x| + 5

Answer 1

Given:

The parent absolute function is

$f(x)=|x|$

To find:

The new function if the parent function is translated up by 5 units and vertically stretched by a factor of 3.

Solution:

The translation is defined as

$g(x)=kf(x+a)+b$                .... (1)

Where, k is stretch factor, a is horizontal shift and b is vertical shift.

If 0<k<1, then the graph compressed vertically by factor k and if k>1, then the graph stretch vertically by factor k.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

Parent function is translated up by 5 units. So, b=5

It is vertically stretched by a factor of 3. So, k=3.

There is no horizontal shift. So, a=0.

Now, putting k=3, a=0 and b=5 in (1), we get

$g(x)=3f(x+0)+5$

$g(x)=3f(x)+5$

$g(x)=3|x|+5$       $[\because f(x)=|x|]$

Therefore, the correct option is D.