To determine which graph represents the function \( y = f(3x) \) based on the parent function \( f(x) = x^2 \), we need to understand how the transformation affects the graph.
The transformation \( y = f(3x) = (3x)^2 = 9x^2 \) compresses the graph horizontally by a factor of \( \frac{1}{3} \). This means any \( x \)-coordinate will be scaled down, resulting in the vertex of the parabola staying at the origin but the points on its sides getting closer together.
Graphically, this results in the parabola appearing narrower than the parent function \( f(x) = x^2 \).
From the descriptions provided:
- Graph 1: x-axis ranges from -5 to 5.
- Graph 2: x-axis ranges from -10 to 10.
- Graph 3: x-axis ranges from -5 to 6.
- Graph 4: (Same as Graph 1) x-axis ranges from -5 to 5.
Graphs that have their x-axis less wide (narrower) as compared to the standard parabola can indicate a horizontal compression.
Considering the x-axis limits, the graph that shows the biggest compression horizontally would be one that has limited x-values to demonstrate this effect.
Without specific images to assess the shape of the graphs, based on the axis ranges, Graph 3, which has an x-axis that ranges from -5 to 6 (which is a total width of 11) and potentially shows a compressed shape, would be the likely candidate for \( y = f(3x) \).
Thus, the correct answer is likely Graph 3.