write a function in any form that would match the graph shown below. answer attempt 1 out of 2 f(x) =
write a function in any form that would match the graph shown below. answer attempt 1 out of 2 f(x) =
Answer
Explanation:
Step1: Identify x - intercepts
The graph has x - intercepts at (x=-2), (x = 1), and (x = 3). A polynomial function with these x - intercepts can be written in factored form (y=a(x + 2)(x - 1)(x - 3)).
Step2: Determine the leading - coefficient
We can assume (a = 1) (since no other information about the vertical stretch is given). Expanding ((x + 2)(x - 1)(x - 3)): First, ((x + 2)(x - 1)=x^{2}-x + 2x-2=x^{2}+x - 2). Then, ((x^{2}+x - 2)(x - 3)=x^{3}-3x^{2}+x^{2}-3x-2x + 6=x^{3}-2x^{2}-5x + 6).
Answer:
(f(x)=(x + 2)(x - 1)(x - 3)) (or (f(x)=x^{3}-2x^{2}-5x + 6))