Final answer:
The equation y=(-4x)/(x²+81) has only one intercept at the origin (0, 0), which is both the x-intercept and y-intercept since the numerator of the fraction equals zero only when x=0.
Step-by-step explanation:
The student has asked to list the intercepts for the equation y=(-4x)/(x²+81). To find the y-intercept, we set x to 0 and calculate y. In this case, y=0 because the numerator becomes 0. Therefore, the y-intercept is (0, 0).
To find the x-intercepts, we set y to 0. Since the denominator cannot be zero (as dividing by zero is undefined), the only way for y to equal 0 is if the numerator is 0 which occurs when x=0. However, since we've already established that (0,0) is the y-intercept, in this case, it also serves as the only x-intercept. Thus, the only intercept for this equation is at the origin (0,0).