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Problem : Are there any functions that are both odd and even?

Yes. The function y = 0 is even and odd.

Problem : Is the function f (x) = 4x even, odd, or neither?

Odd.

Problem : Is the function f (x) = sin(x - ) even, odd, or neither? Use a graphing utility if necessary.

Even.

Problem : Is the function f (x) = x - 5 even, odd, or neither?

Neither.

Problem : What is the inverse of the function y = 3x - 2, and is it a function?

The inverse is y = . It is a function.

Problem : What is the inverse of the function y = , and is it a function?

The inverse is the part of y = x2 + 1 where x≥ 0. It is a function.

Problem : A piecewise function is defined this way: f (x) = - x for x < 0, f (x) = x2 for 0≤x≤3, f (x) = 3x for x > 3. What is f (- 7) + f (2) + f (4)?

f (- 7) + f (2) + f (4) = 7 + 4 + 12 = 23.
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