Question

Consider the graphed function. Based on its end behavior, which of the following could be its equation?

Question 13 options:

A)

ƒ(x) = –x4 + 6x3 – 5x2

B)

ƒ(x) = x4 + 6x3 – 5x2

C)

ƒ(x) = x3 + 6x2 – 5x

D)

ƒ(x) = –x3 + 6x2 – 5x

Answer 1

D) ƒ(x) = –x3 + 6x2 – 5x

Explanation:

It passes through the point (5,0).

by verifying if x=5 what would "y" equal in each function:
ƒ(x) = –x4 + 6x3 – 5x2 => -(5)^4 + 6(5)^3 - 5(5)^2 = -625+750 -125 =0 YES

ƒ(x) = x4 + 6x3 – 5x2 => (5)^4 + 6(5)^3 - 5(5)^2= 625 +750 - 125 = 1250 NO

ƒ(x) = x3 + 6x2 – 5x => (5)^3 + 6(5)^2 - 5(5)=125 + 150 - 25 = 250 NO

ƒ(x) = –x3 + 6x2 – 5x => -(5)^3 + 6 (5)^2 - 5 (5) = -125 +150 - 25 = 0 YES

It also passes through the point (3,12)

its A) or D)

ƒ(x) = –x4 + 6x3 – 5x2 => -(3)^4 + 6(3)^3 - 5(3)^2 = -81 +162 - 45 = -36 NO

ƒ(x) = –x3 + 6x2 – 5x => -(3)^3 + 6 (3)^2 - 5 (3) = -27 + 54 - 15 = 12 YES