Question

question 6 of 40
choose which function is represented by the graph.
a. $f(x) = (x - 1)(x + 2)(x + 5)(x + 10)$
b. $f(x) = (x - 5)(x - 2)(x + 1)$
c. $f(x) = (x - 10)(x - 5)(x - 2)(x + 1)$
d. $f(x) = (x - 1)(x + 2)(x + 5)$

Explanation:

Step1: Identify x-intercepts

Graph crosses x-axis at x=-1, 2, 5, 10.

Step2: Match intercepts to factors

x-intercepts correspond to factors (x - a). So factors: (x+1), (x-2), (x-5), (x-10).

Step3: Form the function

Combine factors: \(f(x)=(x+1)(x-2)(x-5)(x-10)\).

Answer:

C. \(f(x)=(x - 10)(x - 5)(x - 2)(x + 1)\)