Asked by Laurie

Confused Please Help! Thanks!

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
Answered by Amy
What are the choices?
Answered by Laurie
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!
Answered by Reiny
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?
Answered by Reiny
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.

Answered by Laurie
So I would say that the answer would be that f can be both odd and even then. Am I correct?
Answered by Reiny
NO, no, no

it is EVEN.

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

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