Answer: D. Horizontal stretch by a factor of 3.
Step-by-step explanation:
Below are some transformations for a function [tex]f(x)[/tex]:
If [tex]f(x)-k[/tex], then it is shifted "k" units down.
If [tex]f(x-k)[/tex], then it is shifted rigth"k" units.
If [tex]-f(x)[/tex], then it is reflected across the x-axis.
If [tex]cf(x)[/tex] and [tex]c>1[/tex], then it is stretched vertically by a factor of "c".
If [tex]f(cx)[/tex] and [tex]0<c<1[/tex], then it is stretched horizontally by a factor of [tex]\frac{1}{c}[/tex].
Based on this, the transformations done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] are:
- It is shifted 7 units down.
- It is shifted rigth 4 units.
- It is reflected over the x-axis.
- It is vertically stretched by a factor of 3.
Therefore, the transformations that was not done to the function [tex]f(x)=x[/tex] to get the function [tex]g(x)=-3(x-4)-7[/tex] is:
Horizontal stretch by a factor of 3.
