\(\displaystyle f(x) = x^2\)

\(\displaystyle g(x) = 9x^2\)

My answer:

Vertical Expansion by \(\displaystyle 9\) OR Horizontal Compression by \(\displaystyle \frac{1}{9}\).

Text Answer:

Vertical Expansion by \(\displaystyle 9\) OR Horizontal Compression by \(\displaystyle \frac{1}{3}\).

Just wondering, how is the compression factor \(\displaystyle \frac{1}{3}\)? Is it because \(\displaystyle 9x^2 = (3x)^2\), therefore \(\displaystyle 3x = \)Horizontal Compression by \(\displaystyle \frac{1}{3}\)?

Also, is a Horizontal Compression by \(\displaystyle \frac{1}{3}\) the same thing as a Horizontal Expansion by \(\displaystyle 3\)? The terms "Expansion" and "Compression" become quite confusing when used with whole numbers and fractions. It's hard to remember which one refers to which.