1. 1-7 functions Goals: Identify a function. Find function values.
Eligible Content:
A / A / A / A

2. Vocabulary
Function – relationship between 2 quantities called the input and output, where each input must have only one output.

3. Different looks of functions
Tables
Mapping
Ordered Pairs
Graphs
Equations

4. Tables Input Output 3 1 5 2 7 9 Input Output 1 4 2 3 Input Output 5 13 1 5 2 7 9
Input
Output 1 4 2 3
Input
Output 5 1 2 3 4
Input
Output -2 6 5 2 3 4 1
Input
Output 3 1 7 9 2 8
Input
Output 1 4 2 3 5

5. Mappings 2 4 6 8 5 3 2 8 8 1 9
yes 2 4 6
yes 6 4 8 9 5 2 8 4 3 6 no 10
yes

6. Ordered Pairs {(2,4),(3,6),(4,8),(5,10)} {(1,6),(1,2),(3,9),(4,7)}
Yes
{(1,6),(1,2),(3,9),(4,7)} No
{(2,5),(3,5),(4,5),(5,5)}
{(4,4),(4,7),(4,9),(4,13)} no

7. Is this relation a function? Explain.
Yes; for each element of the domain, there is only one corresponding element in the range.
Yes; it can be represented by a mapping.
No; it has negative x-values.
No; both –2 and 2 are in the range.

8. Is this relation a function? Explain.
No; the element 3 in the domain is paired with both 2 and –1 in the range.
No; there are negative values in the range.
Yes; it is a line when graphed.
Yes; it can be represented in a chart.

9. Graphs
Vertical Line Test – If a vertical line touches a graph in more than one place it does not represent a function.

10. Graphs
NOT a function

11. Equations
Function Notation – using the symbol f(x) instead of y in an equation.
Instead of y = 2x + 1
we write f(x) = 2x + 1
Nonlinear function – a function whose graph is not a straight line.
Pronounced
“f of x”

12. Examples Evaluate each function with the given value.
f(x) = 2x – 3, find f(-2).
f(-2) = -7
g(x) = -5x, find g(0).
g(0) = 0
h(x) = 1248 – 160x + 16x2, find h(3).
h(3) = 912

13. If f(x) = 2x + 5, find f(3).
A. 8
B. 7
C. 6
D. 11

14. The function h(t) = 180 – 16t2 represents the height of a ball thrown from a cliff that is 180 feet above the ground.
A. Find h(2).
A. 164 ft
B. 116 ft
C. 180 ft
D. 16 ft

15. Practice
Worksheet – “1-7 Skills Practice”

16. Homework
Page 52 #20-25, 27, 28, 33-36