1.2 Functions Determine whether relations between two variables represent functions Use function notation and evaluate functions Find the domains of functions Use functions to model and solve real-life problems Evaluate difference quotients

Definition of a Function: A function is a relation in which each element of the domain (the set of x-values, or input) is mapped to one and only one element of the range (the set of y-values, or output). Function Not a Function One-to-one Function

A Function can be represented several ways: Verbally – by a sentence that states how the input is related to the output. Numerically – in the form of a table or a list of ordered pairs. Graphically – a set of points graphed on the x-y coordinate plane. Algebraically – by an equation in two variables.

Example 1 Input x 2 3 4 5 Output y 11 10 8 1

Example 2 Which of the equations represents y as a function of x? a. b.

Example 3 Let g(2)= g(t)= g(x+2)=

Example 4 : Evaluate the piecewise function when x=-1 and x=0.

Example 5 : Find the domain of each function b. c. d. e.

Example 6 Use a graphing calculator to find the domain and range of the function

Example 7 The number N (in millions) of cellular phone subscribers in the United States increased in a linear pattern from 1995 to 1997, as shown on p.22. Then, in 1998, the number of subscribers took a jump, and until 2001, increased in a different linear pattern. These two patterns can be approximated by the function where t represents the year, with t=5 corresponding to 1995. Use this function to approximate the number of cellular phone subscribers for each year from 1995 to 2001.

Example 8 A baseball is hit at a point 3 feet above the ground at a velocity of 100 feet per second and an angle of 45 degrees. The path of the baseball is given by the function where y and x are measured in feet. Will the baseball clear a 10 foot fence located 300 feet from home plate?

Student Example A baseball is hit at a point 4 feet above the ground at a velocity of 120 feet per second and an angle of 45 degrees. The path of the baseball is given by the function where y and x are measured in feet. Will the baseball clear an 8 foot fence located 350 feet from home plate?

Example 9 For .

Student Example Evaluate for f(-3) f(x+1) f(x+h)-f(x)