Question

Find the x-intercepts and y-intercept of the following function.

Write your answer in coordinate pairs of the form (x, y).
Provide your answer below:
x-intercept: (),()
f(x) = (x+2)(x+3) (3x + 18)
and
y-intercept: 108

Answer 1

To find the x-intercepts, set the function equal to zero and solve for x. The x-intercepts are (-2, 0), (-3, 0), and (-6, 0). The y-intercept is found by setting x=0 in the function and solving for y. The y-intercept is (0, 108).

Step-by-step explanation:

To find the x-intercepts of a function, we need to set the function equal to zero and solve for x. In this case, the function is f(x) = (x+2)(x+3)(3x+18). Setting f(x) = 0, we have (x+2)(x+3)(3x+18) = 0. By applying the zero product property, we can solve each factor separately to find the x-intercepts. The x-intercepts are: (-2, 0), (-3, 0), and (-6, 0).

The y-intercept of a function is the point where the graph intersects the y-axis. To find the y-intercept, we need to set x=0 in the function and solve for y. Substituting x=0 into f(x) = (x+2)(x+3)(3x+18), we get f(0) = (0+2)(0+3)(3(0)+18) = 2*3*18 = 108. Therefore, the y-intercept is (0, 108).

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