Question

Which graph shows the parent function f(x)=x^2 horizontally compressed to form the graph of y=f(3x)
?

Answer 1

To determine how the function \( f(x) = x^2 \) is transformed by a horizontal compression, we should examine the function \( y = f(3x) \).

1. The original function is \( f(x) = x^2 \), which is a parabola that opens upwards.
2. The transformation \( f(3x) \) means that we are compressing the graph horizontally by a factor of \( \frac{1}{3} \). This means that for any given \( x \)-value, the corresponding \( y \)-value occurs at \( \frac{x}{3} \).

Thus, instead of \( y = x^2 \), we have:

\[
y = (3x)^2 = 9x^2
\]

This graph will have the same shape as the original parabola \( y = x^2 \) but will be narrower, reaching the same \( y \)-value at a smaller \( x \) (specifically, at one-third the \( x \)-coordinate).

When looking for the graph of \( y = 9x^2 \), you should look for a parabola that opens upwards and is steeper than \( y = x^2 \).

In summary, to find the graph showing the parent function \( f(x) = x^2 \) compressed horizontally to form \( y = f(3x) \), you want a steeper version of the standard parabola. It would correspond to \( y = 9x^2 \).