Final answer:
The function r(x) = (x²-9) / (x²) does not have a y-intercept since setting x to 0 is undefined. It has two x-intercepts which are found by solving the equation x² - 9 = 0, leading to x-intercepts at x = 3 and x = -3.
Step-by-step explanation:
To find the x-intercept and y-intercept of the rational function r(x) = (x²-9) / (x²), we evaluate the function for the intercepts. For the y-intercept, we set x to 0, but in this case, we cannot do that because the function is undefined at x=0 (division by zero is not allowed). Therefore, there is no y-intercept.
To find the x-intercept(s), we set r(x) to 0 and solve for x. This gives us 0 = (x²-9) / (x²). Multiplying both sides by x² (assuming x is not equal to 0), we get 0 = x² - 9, which can be factored into (x+3)(x-3) = 0. This yields two x-intercepts at x = 3 and x = -3.