1. 3-2 Representing Functions
Algebra Glencoe McGraw-Hill Linda Stamper

2. Some relations are functions. Tri 1 Report Card
In a function, each member of the domain is paired with exactly one member of the range.
Period
Grade 1 4 2 3 5 6
x(domain)
y(range) 1 4 2 3 5 6
Could you have more than one grade for Period 1?
Alphabetical order: domain listed before range!
A=4
B=3
C=2
D=1
F=0

3. I purchased the following items at the store.
Nike Soccer Store
Item
Price 1 12 2 24 5 26
{(1,12), (2,24), (5,26), (1,12), (5,26), (5,26)}
Is the relation a function?
Yes, it is a function, because each member of the domain (item) is paired with exactly one member of the range (price).
1=soccer socks
2=shin guards
3=soccer ball size 3
4=soccer ball size 4
5=soccer ball size 5

4. Is the relation a function? Explain.
Nike Soccer Store
Item
Price 1 12 2 24 5 26 28
{(1,12), (2,24), (5,26), (1,12), (5,28), (5,26)}
No, it is not a function, because item 5 (domain) has more than one price (range).
Could you determine whether it is a function by looking at the ordered pairs?
1=soccer socks
2=shin guards
3=soccer ball size 3
4=soccer ball size 4
5=soccer ball size 5

5. Is the relation a function? Explain.
Mapping x y 4 2 -4 -3 1 4 -5 -3
No, it is not a function, because domain 2 has different ranges.
{(4,1), (2,4), (-4,1), (2,-5), (0,-3), (-3,-3)}

6. Example 1 Is the relation a function? Explain.
domain
range -2 2 -1 1
Yes, it is a function, because for each domain there is only one range.

7. Example 2 Is the relation a function? Explain.
domain
range 2 1 4 6 3
Yes, it is a function, because for each domain there is only one range.

8. Example 3 Is the relation a function? Explain.
domain
range 2 4 1 6 -1
No, it is not a function, because domain 4 has different ranges.

9. Example 4 Is the relation a function? Explain.
domain
range 3 9 6 18 27 12 36
{(3,9), (6,18), (9,27), (3,9), (12,36)}
Yes, it is a function, because each domain has one range.

10. Example 5 Is the relation a function? Explain.
domain
range -3 12 -2 8 -1 4
-12
{(-3,12), (-2,8), (-1,4), (0,0), (-1,4), (-2,8),(-3,-12)}
No, it is not a function, because domain -3 has two ranges.

11. Next you will learn how to identify whether a graph is a function.
When you graph a function, the domain is given by the horizontal axis
and the range is given by the vertical axis.
y (range)
x (domain)
The x is usually called the independent variable and the y is the dependent variable.

12. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point.
y (range)
x (domain)
The line is the graph (do not confuse the coordinate plane as the graph)!
The graph is a function.

13. You can use your pencil to check
You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function.
y (range)
x (domain)

14. The graph is NOT a function.
A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point.
y (range)
x (domain)
The graph is NOT a function.

15. A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point.
y (range)
x (domain)
The graph is a function.

16. The graph is NOT a function.
A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point.
y (range)
x (domain)
The graph is NOT a function.

17. The graph is NOT a function.
A vertical line test is used to determine whether a graph represents a function. A graph is a function if any vertical line intersects the graph at no more than one point.
y (range)
x (domain)
The graph is NOT a function.

18. You can use your pencil to check
You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function.
y (range)
x (domain)
The graph is a function.

19. The graph is NOT a function.
You can use your pencil to check. Keep your pencil straight to represent a vertical line and pass it across the graph. If it touches the graph at more than one point, the graph is not a function.
y (range)
x (domain)
The graph is NOT a function.

20. Function Notation: When a function is defined by an equation, it is often convenient to name the function. Just as x is commonly used as a variable, the letter f is commonly used to name a function. To write a function notation, you use f(x) in place of y.
The symbol f(x) is read as “the value of f at x” or simply “f of x”. It does not mean f times x.
x-y notation
function notation

21. Remember: If you see f(x), g(x), h(x) or any variable _(x) it is the name for the function and it is used in place of y.

22. Think of f(x) as the formal name for y.
Given f(x) = 3x – 2 find f(–4).
Write the function. y
Substitute.
Simplify (right side only)!
Think of f(x) as the formal name for y.

23. Think of g(x) as the formal name for y.
Given g(x) = 3x – 2 find g(a - 3).
Write the function. y
Substitute.
Simplify (right side only)!
Think of g(x) as the formal name for y.

24. Example 6 Given f(x) = –3x + 7 find f(4).
Example 7 Given find g(-21).
Example 8 Given find h(4).
Example 9 Given f(x) = –3x + 7 find f(a – 2).
Example 10 Given h(x) = x2 – 2x find h(2n).

25. y y y Example 6 Example 7 Example 8
Think of g(x) as the formal name for y.
Think of f(x) as the formal name for y.
Think of h(x) as the formal name for y.

26. Example 9 Given f(x) = –3x + 7 find f(a – 2).
Example 10 Given h(x) = x2 – 2x find h(2n).

27. Example 11 Given f(x) = 3x + 7 find 3[f(r)].
Example Given g(x) = x2 – 2x find 2[g(t)].

28. Homework
3-A3 Pages #15-36,45-47,54-55.