Functions

Functions

is it a function?

Function

What is a function

A Function is

a relation is where each input is related to exactly one output

Multiple Choice

What is a function?

• a relation where each input is related to exactly one input

• a relation where each output is related to exactly one input

• a relation where one output is related to exactly one output

• a relation where each input is related to exactly one output.

Multiple Choice

A relation pairs each input with exactly one output is a

• congruence

• similarity

• function

• mathematical equation

Multiple Choice

All of the x values of a relation are called what?

• Domain

• Range

• Relation

• Function

Multiple Choice

All of the y values of a relation are called what?

• Domain

• Range

• Relation

• Function

Functions In Tables

• For each input there is exactly one output

• Looking at a table all of the "x's" should be different

• If the x's are different it is a function

• If the x's are the same it is not a function

Functions In Tables

• For each input there is exactly one output

• Looking at a table all of the "x's" should be different

• If the x's are different it is a function

• If the x's are the same it is not a function

Multiple Select

Which Tables are a Function?

Multiple Choice

Is the relation a function?

• Yes, each input has one output

• No, each input has more than one output

• No, the cost of the movies is different

• Yes, each output has one input

Multiple Choice

Which table represents y as a function of x?

• Table 1

• Table 2

Multiple Choice

Is the following a Function? Explain

• Yes; Each input has exactly one output.

• Yes; At least one input has more than one output.

• No; Each input has exactly one output.

• No; At least one input has more than one output.

Multiple Choice

Is this table a function or not a function? 

• Function

• Not a Function 

Functions In Ordered Pairs

• For each input there is exactly one output

• Looking at "x" all should be different

• If the x's are different it is a function

• If the x's are the same it is not a function

Multiple Choice

Is the following a Function? Explain.

(2,5), (8, -2), (5,6), (9, -2)

• Yes; Each input has exactly one output.

• Yes; At least one input has more than one output.

• No; Each input has exactly one output.

• No; At least one input has more than one output.

Multiple Choice

Which relation is NOT a function?

• {(1,-5), (3,1), (-5,4), (4,-2)}

• {(2,7), (3,7), (4,7), (5,8)}

• {(1,-5), (-1,6), (1,5), (6,-3)}

• {(3,-2), (5,-6), (7,7), (8,8)}

Multiple Choice

Which of the following is not a function?

• {(0,1), (1,2), (2,3), (3,4)}

• {(0,2), (1,3), (4,3), (1,2)}

• {(1,3), (4,2), (2,0), (3,4)}

• {(1,2), (2,2), (3,2), (4,2)}

Multiple Choice

Is this a function?

• Yes

• No

Multiple Choice

Is this a function?

• Function

• Not a Function

Functions In Mapping Diagrams

• For each input there is exactly one output

• If the x's are different it is a function

• If the x's are the same it is not a function

Functions In Mapping Diagrams

• For each input there is exactly one output

• If the x's EACH have ONE LINE

• If the x's have 2 or more lines it is not a function

Multiple Select

Which Diagrams are Functions

Multiple Choice

List the ordered pairs

• (1,3), (2,6), (3,9), (4,12)

• (3,1), (6,2), (9,3), (12,4)

• Input and Output

• Output and Input

Multiple Choice

Determine if the relations is a function and describe the pattern

• Yes it is a function, input goes up 1 and output goes up by 15

• Yes it is a function, input goes up 15 and output goes up by 1

• Not a function, input goes up 1 and output goes up by 15

• Not a function, input goes up by 15 and output goes up by 1

Multiple Choice

Determine if the relation is a function

• Yes, each input has one output

• Yes, each output has one input

• No, because the pattern is 4

• No, each input is the same as the output

Multiple Choice

Which relation represents y as a function of x?

• Mapping #1

• Mapping #2

Multiple Choice

Is the following a Function? Explain

(You may need to click on the picture to see it better)

• Yes; Each input has exactly one output.

• Yes; At least one input has more than one output.

• No; Each input has exactly one output.

• No; At least one input has more than one output.

Multiple Choice

Is this mapping a function or not a function? 

• Function

• Not a Function 

Draw

Represent the following relation as a mapping diagram {(2,7),(-8,1),(1,7),(3,7)}

Functions In Graph

• Must past the VERTICAL LINE TEST

• IF YOU DRAW A VERTICAL LINE ANYWHERE ON THE GRAPH, IT WILL TOUCH THE LINE IN ONLY ONE POINT

Functions In Graph

• Must past the VERTICAL LINE TEST

• IF YOU DRAW A VERTICAL LINE ANYWHERE ON THE GRAPH, IT WILL TOUCH THE LINE IN ONLY ONE POINT

Functions In Graph

• Must past the VERTICAL LINE TEST

• IF YOU DRAW A VERTICAL LINE ANYWHERE ON THE GRAPH, IT WILL TOUCH THE LINE IN ONLY ONE POINT

Multiple Select

Which Graphs are functions?

Multiple Choice

Is the following a Function? Explain

• Yes; Each input has exactly one output. It passes the vertical line test.

• Yes; At least one input has more than one output. It fails the vertical line test.

• No; Each input has exactly one output. It passes the vertical line test.

• No; At least one input has more than one output. It fails the vertical line test.

Multiple Choice

Is this a function? 

• Yes 

• No

Multiple Choice

Which graph does NOT pass the vertical line test?

• Graph 1

• Graph 2

• Graph 3

• Graph 4

Multiple Choice

Is this graph a function or not a function? 

• Function

• Not a Function

Multiple Choice

Does the graph represent a function?

• Yes, because the vertical line test shows there are no repeating input values

• No, because the vertical line test shows there are repeating input values

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

Is it a function?

• It IS a function.

• It IS NOT a function

Multiple Choice

Which graph represents a function?

Multiple Choice

The graph of a relation is shown at the right. Is this relation a function?

• Yes

• No

• Cannot be determined from a graph

Multiple Choice

Which graph shows a relation that is a function?

Multiple Choice

Is this graph a function or not a function? 

• Function 

• Not a Function

Match

Match the following

• Relation

• Domain

• Range

• Mapping

A set of ordered pairs

All x-values within the relation

All y-values within the relation

Illustrates how each x-value is paired with a y-value

• A set of ordered pairs

• All x-values within the relation

• All y-values within the relation

• Illustrates how each x-value is paired with a y-value

Match

Match the following

• Function

• Input

• Output

• Vertical Line Test

A relation in which each element of the domain is paired with only one element of the range

A value substituted for an x-value in a function

The result of substituting a value into a function

The test used on graph to see if a relation is a function.

• A relation in which each element of the domain is paired with only one element of the range

• A value substituted for an x-value in a function

• The result of substituting a value into a function

• The test used on graph to see if a relation is a function.

Multiple Choice

What is a relation?

• When you marry someone.

• Equations that contain parentheses.

• A set of ordered pairs.

• A set of numbers & variables.

Multiple Choice

What is another name for the set of the second numbers of the ordered pairs in a relation?

• Domain

• Function

• Input

• Range

Multiple Choice

What is another name for the set of the first numbers of the ordered pairs in a relation?

• Domain

• Output

• Range

• Function