1. 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

2. 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

3. 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.

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

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

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

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

8. Example 5 : Find the domain of each functionb. c. d. e.

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

10. 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 Use this function to approximate the number of cellular phone subscribers for each year from 1995 to 2001.

11. 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?

12. 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?

13. Example 9
For

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