1.
Which characteristic is correct for the function f(x) =−2x^4+3x^2?
even
neither even nor odd
both even and odd
odd
2.
Graph the functions on the same coordinate plane.
f(x)=7
g(x)=x2+2x−8
What are the solutions to the equation f(x)=g(x)?
Select each correct answer.
−5
−3
3
5
7
f(x) = -2x^4 + 3x^2
If even, then f(x) = f(-x)
f(-x) = -2(-x)^4 + 3(-x)^2 = -2x^4 + 3x^2 = f(x) ⇒ even
f(x) = 7
f(x) = x^2 + 2x - 8
Set these equal
x^2 + 2x - 8 = 7 subtract 7 from both sides
x^2 + 2x - 15 = 0 factor
(x + 5) ( x - 3) = 0
Set each factor to 0
x + 5 = 0 x - 3 = 0
x = -5 x = 3