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Precalculus: Functions

Problems

Types of Functions

Operations of Functions

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 = x 2 + 1 where x≥ 0 . It is a function.

Problem : A piecewise function is defined this way: f (x) = - x for x < 0 , f (x) = x 2 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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