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How do you determine if #y= 3 + 2x# is an even or odd function?

Answer 1

Theodore Amidon

#color(blue)("Neither")#

For odd and even functions we have:

A function is even if:

#f(x)=f(-x)#

A function is odd if:

#-f(x)=f(-x)#

If none of these is true then the function is neither odd nor even.

So:

#f(x)=f(-x)#

#3+2x=3+2(-x)#

#3+2x=3-2x# This is false, the function is not even.

#-f(x)=f(-x)#

#-(3+2x)=3+2(-x)#

#-3+2x=3-2x# This is also false. The function is neither odd nor even.

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Answer 2

Elias Ackerman

To determine whether the function y = 3 + 2x is even or odd, we can apply the definitions of even and odd functions:

Even functions satisfy the condition f(x) = f(-x) for all x in the domain.
Odd functions satisfy the condition f(x) = -f(-x) for all x in the domain.

For the function y = 3 + 2x:

Even function test: (3 + 2x) ≠ (3 + 2(-x)) This function does not satisfy the condition f(x) = f(-x), so it is not even.
Odd function test: (3 + 2x) ≠ -(3 + 2(-x)) This function also does not satisfy the condition f(x) = -f(-x), so it is not odd.

In conclusion, the function y = 3 + 2x is neither even nor odd.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.