1. Function And Relations Review
f(x)
Vertical Line Test

2. Relations and Functions
Relation: a set of ordered pairs.
{(3, 2), (–1, 5), (0, 2)}
Domain: all of the x values or inputs
{3, –1, 0}
Range: all of the y values or outputs
{2, 5, 2}

3. Function: a relation in which each element of the domain is paired with exactly one element of the range.
Are the following relations also functions?
Ex. {(2, 3), (–1, 4), (4, 5), (–2, 3)}
Yes, each element of the domain is paired with 1 element of the range.
Ex. {(4, 4), (–2, 3), (4, 2), (3, 4)}
No, 4 in the domain is paired with 2 different outputs.

4. Example: Which mapping represents a function? a. b.– – –2
Yes No, –1 is paired with two elements of the range

5. This graph represents a function
Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point.
Example: Do the following graphs represent functions?
hits twice
hits only once
This graph represents
a function
This graph is
not a function

6. 4.2 Perform Function Operations and Composition
Pg. 112
f(x)
Vertical Line Test

7. Function Operations
You can perform operations, such as addition, subtraction, multiplication, and division, with functions…
For example: If f(x) = 3x and g(x) = x – 5
f(x) + g(x) = 3x + (x – 5) =
f(x) – g(x) = 3x – (x – 5)
f(x) • g(x) = (3x)(x – 5)
What about f(x) ÷ g(x) ???????

8. Set the denominator equal to zero. x – 5 = 0
Fraction can not be simplified (they are factors) BUT we can tell where the domain is restricted !!!!!
Set the denominator equal to zero.
x – 5 = 0
Therefore, D: All Real Numbers except where x = 5 or
The denominator tells us the domain of the function

9. Find the following.
where

10. Composition of Functions
Functions can be put together in a composite function that looks like this… f(g(x)) or (f ° g)(x)=
“f of g of x” 2
+ 4 2x 2

11. Evaluating functions: Example: If f(x) = 3x – 1, find f(5)
“f of x” is a function. Find “f of 5”.
f(5) = 3(5) – substitute 5 for x
= 15 – 1
therefore, f(5) = 14

12. Example: If g(x) = 3x2 – 2x find g(–2)
Substitute –2 for each x
g(–2) = 3(–2)2 – 2(–2)
= 3(4) =
g(–2) = 16

13. Examples: If f(x) = x2 – 5 and g(x) = 3x2 + 1 find f(g(2)) and g(f(2))

14. Example: If f(x) = x2 + 6 and g(x) = 3x – 4 find f(g(x))
F(g(x)) = Put g(x) in for the (x) in f(x)

15. Homework
Pg. 114, 1 – 24 all