1. **State the problem:** Find the intercepts of the function $$y=\frac{8x}{x^2+36}$$. 2. **Recall intercept definitions:** - **x-intercepts** occur where $$y=0$$. - **y-intercepts** occur where $$x=0$$. 3. **Find x-intercepts:** Set $$y=0$$: $$0=\frac{8x}{x^2+36}$$ Since the denominator $$x^2+36$$ is always positive (never zero), the numerator must be zero: $$8x=0$$ $$x=0$$ 4. **Find y-intercept:** Set $$x=0$$: $$y=\frac{8\cdot0}{0^2+36}=\frac{0}{36}=0$$ 5. **Conclusion:** The function has one intercept at the origin: $$(0,0)$$. This means the graph crosses the origin.