1. **Problem Statement:** We are given two functions: $$f(x) = \frac{1}{3}x, \quad x \leq 3$$ and a function $g(x)$ whose graph is a parabola opening upwards with vertex at the origin and passing through points (-1,1) and (1,1). We need to sketch the graph of the composite function $g(f(x))$. 2. **Understanding the Functions:** - The function $f(x) = \frac{1}{3}x$ is a linear function with slope $\frac{1}{3}$ defined only for $x \leq 3$. - The function $g(x)$ is a parabola with vertex at (0,0) and points (-1,1), (1,1), which matches the standard parabola $g(x) = x^2$. 3. **Formula for Composite Function:** The composite function $g(f(x))$ means we substitute $f(x)$ into $g$: $$g(f(x)) = (f(x))^2$$ 4. **Substitute $f(x)$ into $g(x)$:** $$g(f(x)) = \left(\frac{1}{3}x\right)^2 = \frac{1}{9}x^2$$ 5. **Domain Consideration:** Since $f(x)$ is defined for $x \leq 3$, the domain of $g(f(x))$ is also $x \leq 3$. 6. **Summary:** - The graph of $g(f(x))$ is a parabola opening upwards. - It is vertically compressed by a factor of $\frac{1}{9}$ compared to $g(x) = x^2$. - The domain is restricted to $x \leq 3$. 7. **Final expression:** $$\boxed{g(f(x)) = \frac{1}{9}x^2, \quad x \leq 3}$$ This is the graph to sketch on the blank coordinate grid.