1. **State the problem:** We are given a function $f(x)$ whose graph is a straight line passing through the origin and points $(-3,-3)$ and $(3,3)$. We need to find the equation of this function. 2. **Recall the formula for a line:** The general form of a line passing through the origin is $f(x) = mx$, where $m$ is the slope. 3. **Calculate the slope $m$:** The slope is given by the change in $y$ over the change in $x$ between two points: $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-3)}{3 - (-3)} = \frac{6}{6} = 1$$ 4. **Write the function:** Since the slope $m=1$, the function is: $$f(x) = 1 \cdot x = x$$ 5. **Interpretation:** This means the function is the identity function, which passes through the origin and has a positive slope of 1, matching the given points. **Final answer:** $$f(x) = x$$