Question

If function f is vertically stretched by a factor of 2 to give function g, which of the following functions represents function g?
f(x) = 3|x| + 5

A. g(x) = 6|x| + 10

B. g(x) = 3|x + 2| + 5

C. g(x) = 3|x| + 7

D. g(x) = 3|2x| + 5

Answer 1

Answer:

A. g(x) = 6|x| +10

Step-by-step explanation:

The parent function is given as:

f(x) = 3|x| + 5

Applying transformation:

function f is vertically stretched by a factor of 2 to give function g.

To stretch a function vertically we multiply the function by the factor:

2*f(x) = 2[3|x| + 5]

g(x) = 2*3|x| + 2*5

g(x) = 5|x| + 10

Answer 2

Answer: Option A.

Step-by-step explanation:

There are some transformations for a function f(x).

One of the transformations is:

If $kf(x)$ and $k>1$, then the function is stretched vertically by a factor of "k".

Therefore, if the function provided $f(x) = 3|x| + 5$ is vertically stretched by a factor or 2, then the transformation is the following:

$2f(x)=g(x)=2(3|x| + 5)$

Applying Disitributive property to simplify, we get that the function g(x) is:

$g(x)=6|x| +10$