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: Option A.

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`

Answer 2

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

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