Question

Algebra Question:
Is the function f(x) = c, even, odd, or neither? Please help me! Thank you!

Answer 1

@CliffSedge
Can you help me, please?

Answer 2

The constant function?
Is it symmetric about the Y-axis, the X-axis, or the origin?

Answer 3

yes

Answer 4

Right, which one?

Answer 5

I dont know, I have to find out, but dont know how!

Answer 6

Let's take y=f(x) and c=3, so an example of a constant function is y=3.
What does that look like when you graph it?

Answer 7

a horizontal line

Answer 8

Uh huh, so is that horizontal line symmetric about the Y-axis, the X-axis, or the origin?

Answer 9

definition-
even: \(\large f(x)=f(-x) \)
odd: \(\large -f(x)=f(-x) \)

Answer 10

Functions that are symmetric about the Y-axis are even.
Functions that are symmetric about the origin are odd.
Functions that are symmetric about the X-axis aren't really functions.
If there is no symmetry, then it is neither even or odd.

Answer 11

For this one, the domain is [0,infinity)

Answer 12

Another way to tell is from the equation.
Our constant function, y=3 can be written as y=3x^0
That exponent, 0, on the x is an even number, so the function is even.

Answer 13

Wait, for what is the domain [0, ∞)?

Answer 14

for f(x) = c, the graph starts from 0, just Quadrant I

Answer 15

Oh . . .
Well, that changes things.

Answer 16

yeah, thats how the graph is given

Answer 17

Do you think its neither?

Answer 18

You mean it looks like this?

Answer 19

yep!

Answer 20

Oh, if you can't even choose negative values for x then the question is irrelevant.

Answer 21

so its neither! No symmetry, right?

Answer 22

If you look at those definitions posted by ByteMe, you'll see you can't even test f(-x) because -x isn't in the domain!
Right, no symmetry, no evenness or oddness.

Answer 23

yeah, thank u so much, thats what I thought first but just wanted someone to clarify my answer