Question

select the correct answer. each statement describes a transformation of the graph of ( f(x) = x ). which statement correctly describes the graph of ( g(x) ) if ( g(x) = f(-10x) )? a. it is the graph of ( f(x) ) reflected about the x - axis and shrunk or compressed vertically by a factor of 10. b. it is the graph of ( f(x) ) reflected about the y - axis and stretched horizontally by a factor of 10. c. it is the graph of ( f(x) ) reflected about the y - axis and shrunk or compressed horizontally by a factor of 10. d. it is the graph of ( f(x) ) reflected about the x - axis and stretched horizontally by a factor of 10.

Explanation:

Step1: Recall function transformation rules

For $g(x)=f(kx)$: if $|k|>1$, horizontal shrink by $\frac{1}{|k|}$; if $k<0$, reflect over y-axis.

Step2: Identify $k$ for $g(x)=f(-10x)$

Here, $k=-10$, $|k|=10>1$, $k<0$.

Step3: Match to transformation

This means reflection over y-axis, horizontal shrink by $\frac{1}{10}$ (shrunk horizontally by factor 10).

Answer:

C. It is the graph of f(x) reflected about the y-axis and shrunk or compressed horizontally by a factor of 10.