Question

Which function matches the graph?

-5
-2
3/
7
A. f(x) =
(x + 3)(x - 5)(x + 7)²(x - 2)²
B. f(x) = (x - 3)²(x + 5)²(x-7)(x + 2)
C. f(x) = (x - 3)(x + 5)(x - 7)²(x + 2)²
D. f(x) = (x - 3)²(x + 5)(x-7)(x + 2)²
E. f(x) = (x + 3)²(x - 5)(x-7)²(x + 2)

Answer 1

Answer: B

Explanation:

The root at
`x=-5` cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of
`(x+5)`.

The root at
`x=-2` bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of
`(x+2)^2`.

The root at
`x=3` cuts through the x-axis, and has a multiplicity of one. So, it corresponds to a factor of
`(x-3)`.

The root at
`x=7` bounces off the x-axis, and has a multiplicity of two. So, it corresponds to a factor of
`(x-7)^2`.