OSTP - Chapter 4 Functions (Teacher Copy)

Functions Review

Example: Name the domain and range for this relation below

(-5, -3), (-2,0), (1,3), (4,6), (7,9)

Domain (all the x-values): {-5, -2, 1, 4, 7}

Range (all the y-values): {-3, 0, 3, 6, 9}

Definition

A RELATION is a set of ordered pairs (like the x-and y-coordinates are in a "relationship". In addition, all of the x-coordinates are called the DOMAIN and all of the y-coordinates are called the RANGE.

Functions

A relation can be any kind of relationship between sets of numbers, FUNCTIONs are a special kind of relationship where EVERY INPUT MUST HAVE EXACTLY ONE OUTPUT.

In other words, the x-value cannot repeat

Does this graph represent a function?

Vertical Line Test

You can easily determine if a relation is a function by graphing it and doing a vertical line test. Just draw a vertical line (or two) on the graph - if your vertical line ever touches two points of the relation, it's not a function. In other words, the vertical line test proves that none of the x-values repeat, and a relation is a function if none of the domain numbers (x-coordinates) repeat.

Examples

Multiple Choice

On the coordinate plane, which line is the x-axis?

• Horizontal Line (Side to Side)
• Vertical Line (Up and Down)

Multiple Choice

On the coordinate plane, which line is the y-axis?

• Horizontal Line (Side to Side)
• Vertical Line (Up and Down)

Multiple Choice

Which graph shows the correct location for (2, -2)?

Multiple Choice

If you were to plot the point (4, -12) what would be the correct method?

• Up 4, left 12
• Right 4, up 12
• Down 4, left 12
• Right 4, down 12

Multiple Choice

Which graph represents the table?

Multiple Choice

Which graph represents the table?

Multiple Choice

Which graph represents the table?

Multiple Choice

Which table is correct for y=4x+3?

Fill in the Blanks

Multiple Choice

Find the 2 missing OUTPUT values.

• -8 & -12
• 8 & 12
• -8 & 12
• 8 & -12

Multiple Choice

Find the missing y values.

• 6 & 12

• 4 & 12

• 4 & 2

• 6 & 2

Fill in the Blanks

Poll

How did you feel about answering these questions?

• Great!

• Good

• Okay

• Terrible

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

• Function
• Not a Function

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1
• Graph 2
• Graph 3
• Graph 4

Multiple Choice

y=x-6

What is the missing number?

• 12

• 10

• 14

• 13

Multiple Choice

If my function rule is 4x, what is the OUTPUT if the input is 5?

• 45

• 54

• 9

• 20

Multiple Choice

If my function rule is 2x + 1, what is the OUTPUT if the input is 2?

• 5

• 4

• 22

• 23

Multiple Choice

Level 1 Find the missing OUTPUT value.

• 8

• -2

• 2

• -8

Multiple Choice

I began to walk; then, I increased my pace and held it constant for a period of time and then decreased my pace slowly. Which graph models this situation?

• A

• B

• C

• D