Transformations

Mar 2010
78
2
State the transformations:
\(\displaystyle f(x) = x^2\)
\(\displaystyle g(x) = 9x^2\)

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.
 

mr fantastic

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State the transformations:
\(\displaystyle f(x) = x^2\)
\(\displaystyle g(x) = 9x^2\)

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.
g(x) can be thought of as either 9f(x) or f(3x) ....