1. solution set (describes all values that make an equation true.)
Functions
f(x)=2x-7
Domain & Range
solution set (describes all values that make an equation true.)
Graphing an equation is the simplest way to recognize the solution set.
g(x)=x+12

2. ( horizontal number line)-5 5 10
-10
Positive #’s
y-axis
(vertical number line)
RANGE
negative #’s
Positive #’s
x-axis
( horizontal number line)
negative #’s
HORIZONTAL
DOMAIN 2

3. y Range x Domain domain of the function ( set of values of x)
range of the function (set of values of y ).
y ≥ -3
Ex: Find the domain & range of the graph. x y 4 -4
Range
Domain
all real numbers.
f (x) = x2 – 2x – 2 3

4. domain : all real numbers range :all real numbers.
Graph y=5x. Looking at the graph of a function can help you determine its domain and range.
All y-values
y =5x
All x-values
domain : all real numbers
range :all real numbers. 4

5. y Range (-3, 0) x Domain f (x) =
Ex: Find the domain and range from its graph.
domain : x ≥ -3
range is y ≥ 0 x y
Range
(-3, 0)
Domain
f (x) = 5

6. Identifying Functions
Give the domain and range of the relation. Tell whether the relation is a function. Explain.
Draw in lines to see the domain and range values.
Range
D: –5 ≤ x ≤ 3
R: –2 ≤ y ≤ 1
To compare domain & range values, make a table using the points from the graph.
Domain x –2 –1 y 1
The relation is not a function. Nearly all domain values have more than one range value.
To find the domain & range from a graph, it may help to draw lines to see the x- and y-values.
Helpful Hint

7. Range: y > 0
y =|x|
Domain: ∞ or all real #s 7

8. Showing Multiple Representations of Relations
Express the relation {(2, 3), (4, 7), (6, 8)} as a table, as a graph, and as a mapping diagram.
Mapping Diagram
Use x- & y-values to plot ordered pairs.
x y
Table x y 2 6 4 3 8 7 2 4 6 3 7 8
x-values under “x”
y-values under “y”. Draw an arrow from each x-value to its corresponding y-value.
Write all x-values under “x” & all y-values under “y”.

9. Is the relation a function?
{(2,4),(3,6),(4,8)}
{(2,4),(3,4),(4,4)}
{(2,4),(2,6),(2,8)}
{(2,5),(3,7),(4,9)}
YES
YES NO
YES 9

10. Relations Different ways to represent a relation.
GIVEN: {(3, 3), (-1, 4), (0, -4)}
Ordered Pairs
Table
Graph
Mapping
(3, 3)
(-1, 4)
(0, -4)
mapping - an illustration how each element of domain is paired with an element in the range. 10