Question

PLEASE HELP WILL GIVE BRAIN Which could be the function of the following graph?

f(x) = (x + 5)^3(x + 1)^2(x - 2)^2 f(x)=(x+5)3(x+1)2(x−2)2

f(x) = (x + 5)^2(x + 1)(x - 2)^3 f(x)=(x+5)2(x+1)(x−2)3

f(x) = (x + 5)^3(x + 1)^2(x - 2)^2(x - 5) f(x)=(x+5)3(x+1)2(x−2)2(x−5)

f(x) = (x + 5)(x + 1)^3(x - 2)^2

Answer 1

C

Explanation:

Answer 2

• Close options are B and D but no matching function

Explanation:

The graphed function has:

• Even degree because overall U-shaped
• Three x-intercepts (-5, -1, 2)
• There is one y-intercept (-5)

The answer options:

f(x) = (x + 5)^3(x + 1)^2(x - 2)^2

• Has degree of (3 + 2 + 2) = 7 - incorrect

f(x) = (x + 5)^2(x + 1)(x - 2)^3

• Has degree of (2 + 1 + 3) = 6 - correct
• x- intercepts are (-5, -1, 2) - correct
• y- intercept is (-200) - incorrect

f(x) = (x + 5)^3(x + 1)^2(x - 2)^2(x - 5)

• Has degree of (3 + 2 + 2 + 1) = 8 - correct
• x- intercepts are (-5, -1, 2, 5) - incorrect

f(x) = (x + 5)(x + 1)^3(x - 2)^2

• Has degree of (1 + 3 + 2) = 6 - correct
• x- intercepts are (-5, -1, 2) - correct
• y- intercept is (24) - incorrect