Question

Which statement best describes the effect of replacing the function f(x) = 2x − 2 with the function g(x) = 2x + 5?

The graph shifts 7 units left.
The graph shifts 5 units left.
The graph shifts 2 units up.
The graph shifts 3 units up.

Answer 1

The statement which best describes the effect of replacing the function f(x) with g(x) is:

The graph shifts 7 units up.

Explanation:

The function f(x) is given by :

`f(x)=2x-2`

The function f(x) is a linear function with positive slope.

and the function g(x) is given by:

`g(x)=2x+5`

The function g(x) is a linear function with same positive slope.

Also, we know that any transformation of the type:

f(x) → f(x)+k

is a translation transformation such that it if k>0 then it is a shift k units upwards and if k<0 then it is a shift k units downward.

Here we have:

g(x)=2x+5-2+2

i.e.

g(x)=2x-2+7

i.e.

g(x)=f(x)+7

Hence, the function g(x) is a translation of the function f(x) 7 units upward.