Question

Determine algebraically whether the function is even, odd, or neither even nor odd.

f(x) = 3x^2 - 1

Answer 1

A function is even if it's made up of only polynomials with even power terms

The trick to this would be to recognize that constants are really multiplied by x^0 which is 1.

Answer 2

if f(-1) = f(1) we say its even

if f(-1) = -f(1) we say its odd

if neither, then neither

Answer 3

but it's negative 1

Answer 4

so its even?

Answer 5

to be more general, use f(a) instead of f(1) but numbers tend to be eaiser to play with

Answer 6

It is symmetrical across the y-axis it's even. If you can rotate it by 180 degrees, then it's odd.

Answer 7

so it's neither...?

Answer 8

if its even then it will have symmetry with respect to the y axis

Answer 9

look at your graph, that will tell you if its even or not