Question

Find the x- and y-intercepts of the rational function. (If an answer does not exist, enter DNE.)

r(x) = x³ + 64/x² + 16
x-intercept (x, y) = (▭)
y-intercept (x, y) = (▭)

Answer 1

To find the x-intercepts, set the numerator equal to zero and solve for x. The x-intercepts are -4 and 2 ± 2i. The y-intercept does not exist.

Step-by-step explanation:

To find the x-intercepts of the rational function, we set the numerator equal to zero and solve for x. In this case, x³ + 64 = 0.

We can factor the equation as (x + 4)(x² - 4x + 16) = 0.

Therefore, the x-intercepts are x = -4 and x = 2 ± 2i.

To find the y-intercept, we set x equal to zero and solve for y. In this case, when x = 0, the equation becomes y = 0³ + 64/0² + 16*0.

Since division by zero is undefined, the y-intercept does not exist (DNE).