Confused Please Help! Thanks!

Question

Let f(x) = 1 – 3x^2. Which of the following is true? Give a brief explanation.

A. f is an odd function
B. f is an even function
C. f is neither odd nor even
D. f is both odd and even

Answer 1

What are the choices?

Answer 2

A. f is an odd function
B. f is an even function
C. f is neither odd nor even
D.f is both odd and even

Totally confused and would appreciate some insight. Thanks!

Answer 3

an even function is one where f(x) = f(-x), that is, using either a positive number as input to the function you get the same result as if you used the opposite of that number

and odd function is where f(x) = -f(x)

so what if you tried f(5) and f(-5)
f(5) = 1 - 3(5)^2 = 1 - 75 = -74
f(-5) = 1 - 3(-5)^2 = 1 - 75 = -74

will that be true for all ± x's ?

mmmhhh?

Answer 4

another way to look at it:

an even function results in a reflection in the y-axis

an odd function results in a reflection in the origin.

Answer 5

So I would say that the answer would be that f can be both odd and even then. Am I correct?

Answer 6

NO, no, no

it is EVEN.

Just make a quick sketch of the graph.
Did you not read my explanations ?

Answer 7

Yes I read them, but misinterpreted them I suppose.

So this is an even function because x is being represented rather than y and this would be an even function resulting in a reflection in the y-axis?

I will sketch it out.

Answer 8

If this was a -f(x) then it would be odd? I think I understand now..Am I correct?