1. Lesson 7-2 Functions and Graphs To learn the definition of function
To learn about properties and geometric representations of functions.
Lesson 7-2

2. You can write rules to show the relationship between input and output values using a
Table
Equation
Graph
Diagram

3. Each table represents a relation
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
Input
Output -2 -3 -1 1 3 2 5 7 4 9
Table 2
Input
Output 4 -2 1 -1 2 9 3 16
Table 3
Input
Output -2
0.44 -1
0.67 1
1.5 2
2.25 3
3.37 4
5.06
Table 4
Input
Output -2 -3 -1 -5 1 2
-10 3 -8

4. Each algebraic statement below represents a relation
Each algebraic statement below represents a relation. Based on the equations, which relations are functions and which are not? Give reasons for your answer.

5. Each graph below represents a relation
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.

6. 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.

8. Name the form of each linear equation or inequality, and use a graph to explain why it is or is not a function.
y=a+bx form
Intercept form
y=mx +b form
Slope intercept form
y=kx form
Direct variation
All three equations and graphs represent functions because every x input corresponds with exactly one y output.

9. Name the form of each linear equation or inequality, and use a graph to explain why it is or is not a function.
ax +by = c form
Standard form
y=y1 +b(x-x1) form
Point-slope form
y=k form
Horizontal line

10. Name the form of each linear equation or inequality, and use a graph to explain why it is or is not a function.
x= k form
Vertical line
Boundary line, in standard form, of an inequality