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

Question

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

GPT-4o mini · Answer

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 $.