The cubic polynomia function f(x) = (x+2) (x+3) (x-2) best represents the graph where it falls to the left and rises to the right with x-intercepts -3,-3, and 2.
The graph of the polynomial function falls to the left and rises to the right where x-intercepts are (0, -3), (0, -2), and (0, 2).
We have to see which cubic polynomials function given in the option conforms with the given statement.
What is the x-intercept of a function?
The x-intercept of a function is the points on the x-axis of the graph where the function passes.
We consider y = 0 or f(x) = 0 when we find the x-intercept.
Finding the x-intercept for all the given options.
1. f(x) = (x − 2)(x − 3)(x + 2)
Put f(x) = 0.
0 = (x-2)(x-3)(x+2)
x-2 = 0. x-3 = 0. x+2 = 0
x = 2. x = 3. x = -2
x = 2, 3, -2
x-intercepts are 2, 3, and -2.
Similarly,
2. f(x) = (x + 2)(x + 3)(x + 12)
x-intercepts are -2, -3 and, -12.
3. f(x) = (x + 2)(x + 3)(x − 2)
x-intercepts are -2, -3, and 2.
4. f(x) = (x − 2)(x − 3)(x − 12)
x-intercepts are 2, 3, and 12
Thus we see that the cubic polynomial function f(x) = (x+2)(x+3)(x-2) have -2, -3 and 2 as its x-intercept.
The graph of this cubic function falls to the left and rises to the right as shown below.
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