1. Algebra 4-6 Functions
Functions
A function is a relation in which each element of the domain is paired with exactly one element of the range.
Functions
Harbour

2. Identify Functions
Determine whether the relation is a function. Explain.
Answer: This is a function because the mapping shows each element of the domain paired with exactly one member of the range.
Example 6-1a

3. Identify Functions
Determine whether the relation is a function. Explain. x y –7
–12 –4 –9 2 –3 5
Answer: This table represents a function because the table shows each element of the domain paired with exactly one element of the range.
Example 6-1b

4. Identify Functions
Determine whether {(–5, 2), (–2, 5), (0, 7), (0, 9)} is a function. Explain.
Answer: This relation is not a function because the element 0 in the domain is paired with both 7 and 9 in the range.
Example 6-1c

5. Identify Functions
Determine whether each relation is a function. Explain. a.
Answer: This mapping represents a function since, for each element of the domain, there is only one corresponding element in the range.
Example 6-1d

6. Identify Functions Y X b. c. {(3, 0), (1, 2), (4, 0), (5, –1)} –1 3 –4–2 1 Y X
Answer: This relation is not a function because the element 3 in the domain is paired with both 2 and –1 in the range.
Answer: This is a function because the mapping shows each element of the domain paired with exactly one member of the range.
Example 6-1d

7. Algebra 4-6 Functions
Functions
You can use the vertical line test to see if a graph represents a function.
If no vertical line can be drawn so that it intersects the graph no more than once, then the graph is a function.
If a vertical line can be drawn so that it intersects the graph at two or more points, the relation is not a function.
Functions
Harbour

8. One way to perform the vertical line test is to use a pencil.
Algebra 4-6 Functions
Functions
One way to perform the vertical line test is to use a pencil.
Functions
Harbour

9. Equations as Functions
Determine whether is a function.
Graph the equation. Since the graph is in the form the graph of the equation will be a line. Place your pencil at the left of the graph to represent a vertical line. Slowly move the pencil to the right across the graph. At this vertical line passes through more than one point on the graph.
Answer: The graph does not pass the vertical line test. Thus, the line does not represent a function.
Example 6-2a

10. Equations as Functions
Determine whether is a function.
Answer: yes
Example 6-2b

11. equation function notation
Functions
Algebra 4-6 Functions
Equations that are functions can be written in a form called function notation.
equation function notation
range
domain
Functions
Harbour

12. Function Values If find . Replace x with 4. Multiply. Subtract.
Answer:
Example 6-3a

13. Function Values If find . Replace x with –5. Multiply. Subtract.
Answer:
Example 6-3b

14. Function Values If find . Replace x with 2 – x. Distributive Property
Simplify.
Answer:
Example 6-3c

15. Function Values If find each value. a. b. Answer: 11 c. Answer: –11
Example 6-3d

16. Some functions are not linear.
However, you can still find values of these functions.
Nonlinear Function Values
If , find .
Replace m with –3.
Multiply.
Simplify.
Answer:
Example 6-4a

17. Nonlinear Function Values
If , find .
Replace m with 6z.
Simplify.
Answer:
Example 6-4b

18. Nonlinear Function Values
If , find .
Evaluate k(y) by replacing m with y.
Multiply the value of k(y) by –4.
Simplify.
Answer:
Example 6-4c

19. Nonlinear Function Values
If find each value. a. b. c.
Answer: 8
Answer:
Answer:
Example 6-4d

20. Nonstandard Function Notation
Multiple-Choice Test Item
A B C D 81 If
Read the Test Item
The symbol is just a different notation for f(x).
Solve the Test Item
Replace x with –5.
Think: .
Replace x with –5.
Simplify.
Answer: A
Example 6-5a

21. Nonstandard Function Notation
Multiple-Choice Test Item
A B C D 19 If
Answer: C
Example 6-5b