Relations vs. Functions

Relations vs. Functions

Read over these next few slides to review our lesson on Functions!

Function or Relation (Not a Function?)

Time to practice!

Multiple Choice

Is the relationship in the table a function or not a function?

• Function

• Not a Function (Relation)

Relation (NOT A FUNCTION)

The left column is the inputs (x-values). -2 repeats two times, so this is not a function.

Multiple Choice

Is this a function?
{ (4, 4) (2, 2) (5, 5) (8, 8) }

• Yes
• No

Is this a function?

{ (4, 4) (2, 2) (5, 5) (8, 8) }

YES, THIS IS A FUNCTION!

The x-values are 4, 2, 5, and 8. None of them repeat!

Multiple Choice

Is this a function?
{ (-1, 0) (7, 4) (-5, 2) (-1, 5) }

• Yes
• No

Is this a function?

{ (-1, 0) (7, 4) (-5, 2) (-1, 5) }

NO, THIS IS NOT A FUNCTION!

The x-values are -1, 7, and -5. The value -1 repeats two times, so this is not a function.

Multiple Choice

Is this a function?

• Yes
• No

NO, THIS IS NOT A FUNCTION

The input (x-value) 4 has two arrows pointing away from it. It has more than one output.

Multiple Choice

Is this a function?

• Yes

• No

YES, THIS IS A FUNCTION

Even though all the inputs go to the same output, each input only has ONE ARROW going away from it.

Multiple Choice

Is this graph a function?

• YES

• NO

YES, THIS IS A FUNCTION

It passes the vertical line test. Each vertical line only touches the graph once.

Multiple Choice

Is this graph a function?

• YES

• NO

NO, THIS IS NOT A FUNCTION

It does not pass the vertical line test. The graph touches one vertical line in two different places.

Multiple Choice

Is this relation a function?

• YES

• NO

NO, IT IS NOT A FUNCTION

Two points are on the same vertical line (fails the vertical line test).

Multiple Choice

Is this relation a function?

• YES, no x-values repeat.

• NO, there is a repeating x-value.

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Which graph does NOT pass the vertical line test? A vertical line should only touch one point at a time, if it is a function.

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

Multiple Choice

• This IS a Function
• This is NOT a Function
• This is a linear function
• This is a toaster oven

Multiple Choice

• Function
• Not a Function
• Venn Diagram
• T - Table

Multiple Choice

Look at this set of ordered pairs: (4, 13), (1, 12), (6, 9)

Is this relation a function?

• Yes

• No

Multiple Choice

Which of these relations is a function?

Multiple Choice

Does this mapping diagram represent a function?

• No, because there are repeating input values
• Yes, because there are no repeating input values

Multiple Choice

Which set of ordered pairs represents a function?

• {(3, 2), (4, 4), (6, 3), (4, 5)}

• {(4, –3), (4, –1), (4, 3), (4, 6)}

• {(–4, 4), (–2, 4), (1, 4), (5, 4)}

• {(–3, –3), (–2, –4), (–2, –1), (–1, –5)}