To identify the graph representing the function \( y = f(3x) \) which is a horizontally compressed version of the parent function \( f(x) = x^2 \), we need to recognize that applying \( f(3x) \) compresses the graph horizontally by a factor of 1/3.
The key characteristics of the vertically symmetrical parabola \( f(x) = x^2 \) centered at the origin will narrow when transformed into \( y = f(3x) \). Specifically, instead of the points (1,1) and (-1,1) which are typical for \( f(x) \), the transformed function will reach the same y-values more quickly since it’s compressed.
If we visualize or calculate, points on the graph of \( y = (3x)^2 \) yield:
- At \( x = \frac{1}{3} \), \( y = 1 \)
- At \( x = -\frac{1}{3} \), \( y = 1 \)
Thus, the graph must show that the parabola rises more steeply compared to the standard \( f(x) \).
Referencing the options provided, look for:
- A narrower graph in relation to the x-axis — particularly one that has its key points and symmetrical properties occur closer to the y-axis, specifically between -1 and 1 in the x-range.
Choose the one that shows this horizontal compression effect by focusing on the x-axis range. If there is a graph that has a range significantly narrower than the typical whole number range of -5 to 5 or -10 to 10 (like potentially the one ranging from -5 to 6), then this is likely the correct answer.
Without seeing the images themselves, I would recommend looking for the graph with the x-values that fit these criteria for the transformation applied \( f(3x) \). The compressed graph will likely have a smaller x-axis range relative to the y-values.