Answer:
The statement which best describes the effect of replacing the function f(x) with g(x) is:
The graph shifts 7 units up.
Step-by-step explanation:
The function f(x) is given by :
[tex]f(x)=2x-2[/tex]
The function f(x) is a linear function with positive slope.
and the function g(x) is given by:
[tex]g(x)=2x+5[/tex]
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.
