Which function could be shown in the graph below? A. f(x) = -3x^4+x^2-5 B. f(x) = x^4-5x^2+4 C. f(x) = 4x^3-12x^2-x+15 D. f(x) = x^5-3x^2+2x

Question

Which function could be shown in the graph below?

A.
`f(x) = -3x^4+x^2-5`
B.
`f(x) = x^4-5x^2+4`
C.
`f(x) = 4x^3-12x^2-x+15`
D.
`f(x) = x^5-3x^2+2x`

Answer 1

B

Explanation:

Answer 2

B.
`f(x) = x^4-5x^2+4`

Explanation:

The graph of the given function falls at the left side and rises on the right,

This means that the degree of the function represented by the graph must be even and the leading coefficient must be positive.

The y-intercept of the graph is also 4.

Using the end behavior and the y-intercept the function represented in the graph should be
`f(x) = x^4-5x^2+4`

The correct choice is B.