Question

Find the x-intercept(s) at which f crosses the axis. express the intercept(s) as ordered pair(s).

Answer 1

The x-intercepts of the function are (-4, 0), (3, 0), (2, 0)

how to find the x-intercepts?

Here we have the function:

f(x) = (x + 4)²*(x - 3)³(x - 2)

Now, the x-intercepts are the values of x such that f(x) = 0, here is trivially that we can see that the zeros of the function are when:

(x + 4) = 0, or (x - 3) = 0, or (x - 2) = 0

So the x intercepts are:

x = -4

x = 3

x = 2

Written as points, these are: (-4, 0), (3, 0), (2, 0)

Answer 2

To find the x-intercepts of the function, set f(x)=0 and solve for x as shown below

`\begin{gathered} f(x)=0 \\ \Rightarrow(x+4)^2(x-3)^3(x-2)=0 \\ \end{gathered}`

When x=-4, the first term is equal to zero; if x=3, the second term is zero, and when x=2, the third and final term is zero.

Therefore, the x-intercepts are at x=-4,3,2 (the roots of the function).

Thus, the answers are x=-4, x=3, and x=2 (points (-4,0), (3,0), and (2,0))