Download Lesson 7.2

Functions and Graphs
•
•
To learn the definition of function
To learn about properties and geometric representations of
functions.
LESSON 7-2
You can write rules to show
the relationship between
input and output values
using a
•
Table
•
Equation
•
Graph
•
Diagram

Each table represents a relation. Based
on the tables, which relations are
functions and which are not? Give a
reason for your answer.
Table 1
Table 2
Table 3
Table 4
Input
Output
Input
Output
Input
Output
Input
Output
-2
-3
4
-2
-2
0.44
-2
-3
-1
-1
1
-1
-1
0.67
-1
-5
0
1
0
0
0
1
1
-1
1
3
1
1
1
1.5
1
-3
2
5
4
2
2
2.25
2
-10
3
7
9
3
3
3.37
3
-2
4
9
16
4
4
5.06
3
-8

Each algebraic statement below represents a
relation. Based on the equations, which
relations are functions and which are not?
Give reasons for your answer.
Statement 1
y  1  2x
Statement 2
y2  x
Statement 3
y  1.5x
Statement 4
2
y  1  x
3
Each graph below represents a relation. Move a
vertical line, such as the edge of a ruler, from
side to side on the graph. Based on the graph
and your vertical line, which relations are
functions and which are not? Give reasons for
your answer.
Graph 1
Graph 2
Graph 3
Graph 4
Use your results to write a rule explaining how
you can determine whether a relation is a
function based on its graph.
A function is a relation
between input and output
values.
 Each input has exactly one
output.
 The vertical line test helps
you determine if a relation
is a function.
 If all possible vertical lines
cross the graph once or not
at all, then the graph
represents a function.

Name the form of each linear equation or
inequality, and use a graph to explain why it is
or is not a function.
y  1  3x
y=a+bx form
Intercept form
y  0.5x  2
y=mx +b form
Slope intercept form
y 
3
x
4
y=kx form
Direct variation
All three equations and graphs represent
functions because every x input
corresponds with exactly one y output.
Name the form of each linear equation or
inequality, and use a graph to explain why it is
or is not a function.
2x  3y  6
y  5  2(x  8)
ax +by = c form
Standard form
y=y1 +b(x-x1) form
Point-slope form
y 7
y=k form
Horizontal line
Name the form of each linear equation or
inequality, and use a graph to explain why it is
or is not a function.
x 9
x= k form
Vertical line
2x  4y  12
Boundary line, in
standard form, of
an inequality