3.1 Functions

Determining Inputs and Outputs The cost of a tank of gas depends on the number of gallons purchased. The volume of a cube depends on the length of its edges. The amount of income tax you pay depends on your income.

Definition of a Function A function consists of – A set of inputs (domain) – A rule by which each input determines one and only one output – A set of outputs (range)

Determine if Relation is a Function Inputs Outputs56789 Inputs13579 Outputs55785

Evaluating a Function Find the indicated values of g(x) = 3x – g(3) – g(-5) – g(0)

Finding a Difference Quotient For f(x) = 3x 2 – 2x and h ≠ 0, find each output. – f(x + h) – f(x + h) – f(x) – f(x + h) – f(x) / h (Difference Quotient)

Functions Defined by Equations Determine whether each equation defines y as a function of x. – 2y 3 – 32x + 11 = 0 – 2x + y 2 – 3 = 0 Solve for y. Make sure you get exactly one y for every x.

Domain Unless otherwise stated, the domain consists of every real number input that produces a real number output. Find the domain for each function. – k(x) = 3 / (x + 4) – f(w) = square root( 1 – x)

Piecewise-Defined Functions For the piecewise-defined function f(x) = 3x 2 – 5 if x ≥ 4 2x + 15 if x < 3 Find each of the following: a. f(0) b. f(4) c. f(3.5)

Greatest Integer Function For any number x, round down to the nearest integer less than or equal to x. Written f(x) = [x] Let f(x) = [x]. Evaluate the following: a. f(4.5) b. f(-3) c. f(0)

Problems p , 2, 5-8, 14, 17, 20, 23, 27, 30, 31, 43, 44, 52, 53, 57, 58, 63, 65, 71