Function & Function Operations

​Functions & Function Operations

​Dr. Tom Giles

Vocab

• Function: a relation in which each element of the domain is mapped to (paired with) exactly one element of the range

• Domain (x): the set of input values for which a function is defined

• Range (y): the set of output values corresponding to the domain values

• Relation: a set of ordered pairs

• Independent Variable: the variable in a function that represents the input values; the first coordinate in an ordered pair - the x value

• Dependent Variable: the variable in a function that represents the output values; the second coordinate in the ordered pair - the y value

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Multiple Choice

• Function
• Not a Function

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

Is this mapping a function or not a function? 

• Function
• Not a Function

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

All of the y values or outputs are called what?

• Domain
• Range
• Relation
• Function

Multiple Choice

Does this mapping diagram represent a function?

• No, because an input value goes to multiple output values
• Yes, because each input goes to one and only one output

Multiple Choice

All of the x values or inputs are called what?

• Domain
• Range
• Relation
• Function

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 of these is NOT the same

• Range
• Input
• Dependent Value
• Y-Value

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function 

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

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function 

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

Is this table a function or not a function? 

• Function
• Not a Function

Multiple Choice

What is the definition of function?

• Has inputs and outputs
• Every input has only ONE output
• Inputs have different outputs every time
• x-values and y-values

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

.

• Function
• Not a Function

Multiple Choice

Which set of values is a function?

• (9,5) (10,5) (9,-5) (10,-5)
• (3,4) (4,-3) (7,4) (3, 8)
• (6,-5) (7, -3) (8, -1) (9, 1)
• (2, -2) (5, 9) (5, -7) (1, 4)

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function 

Multiple Choice

Is it a function?

• Yes
• No

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

• D: {1, -3, -4,}
  R: {0, 1, 2, -4}
• D:{0, 1, 2, -4}
  R:{1, -3, -4}
• D:{0, 1, 2, 3, 4}
  R:{1, -3, -4}

Multiple Choice

Is this graph a function or not a function? 

• Function
• Not a Function

Multiple Choice

What is the range of the following graph?

• all real numbers
• all integers
• any real number greater than zero
• it can not be determined

Multiple Choice

Which ordered pair could you add to the following list of points to create a function?  (3, 5) (4, 9) (2, 5) 

• (3, 7)
• (4, 1) 
• (1, 9)
• (2, 6)

Multiple Choice

Does the table represent a function?

• Yes, there  is a repeated x-value. 
• No, there aren't any repeated y-values. 
• Yes, there are repeated y-values. 
• No, there is a repeated x-value. 

Multiple Choice

Is this graph a function or not a function? 

• Function 
• Not a Function

Multiple Choice

Is this set of ordered pairs a function and how can you tell?

• Yes its a function because no y values repeat
• No it's not a function because there are negative numbers
• No it isn't a function because an x value repeats but has different y values 
• No it isn't a function because an y value repeats but has different x values

Multiple Choice

Which graph does NOT pass the vertical line test?

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

Multiple Choice

Which set of values is not a function?

• (9,5) (10,5) (4,-5) (8,-5)

• (3,4) (4,-3) (7,4) (3, 8)

• (6,-5) (7, -3) (8, -1) (9, 1)

• (2, -2) (5, 9) (-5, -7) (1, 4)

Multiple Choice

• Function
• Not a Function

Multiple Choice

Is this graph a function or not a function? 

• 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

What is the domain of the graph?

• -7 ≤ x < 5
• -3 ≤ x < 1
• -3 ≤ y < 1
• -7 ≤ y < 5

Multiple Choice

What is the range?

• -4 < x ≤ 5
• -4 ≤ x < 5
• -3 < y < 3
• -3 ≤ y ≤ 3

​EVALUATING FUNCTIONS

​

SUMMARY​

To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, x). Replace the x with the number or expression, then follow the order of operations​

​LET'S TRY! :)

Multiple Choice

Given that f(x) = 3x + 6, find f(-2).

• 2

• -1

• 0

• 1

Multiple Choice

Given that g(x) = x²  - 5x -12, find g(-5).

• 38

• 18

• 15

• 0

Multiple Choice

Find 4h(3), given that h(x) = $$\frac{x+6}{2}$$  

• 8

• 18

• 15

• 0

Multiple Choice

Given that f(x) = 5 - 2x and g(x) = 5x + 12, find 2f(0) - 3g(-2).

• 6

• 4

• -6

• -4

Multiple Choice

Given that j(x) = 3x -10, what is x if j(x) = 20.

• -5

• 8

• -6

• 10

Multiple Choice

What is the range of the graph?

• -7 ≤ x < 5
• -3 ≤ x < 1
• -3 ≤ y < 1
• -7 ≤ y < 5

​

SUMMARY​

The graph of a function is a way of viewing the outputs of the function for all possible inputs. Here, we let y=f(x) so that each y-value represents the output and each x-value represents the input. This means any point on the graph is: (x,y)=(input,corresponding output)

​LET'S TRY! :)

Multiple Choice

Given the graph of f. Find f(-1)

• 0

• -1

• 1

• 2

Multiple Choice

Given the graph of f. Find f(2)

• 3

• 2

• 1

• 0

Multiple Choice

Which graph does NOT pass the vertical line test?

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

Multiple Choice

Given the graph of f. Find 3f(-2) + 5f(1)

• -15

• 16

• 17

• -17

Multiple Choice

Given the graph of f. Find f(x) = 0

• 3

• 2

• -1

• 0

Multiple Choice

Given the graph of f. Find f(x) = 1

• (-1, 1)

• {-1, 1)

• (-1, 1}

• {-1, 1}

​

Let's summarize

The graph of a function is a way of viewing the outputs of the function for all possible inputs. Here, we let y=f(x) so that each y-value represents the output and each x-value represents the input. This means any point on the graph is: (x,y)=(input,corresponding output)

To evaluate a function, substitute the input (the given number or expression) for the function's variable (place holder, x). Replace the x with the number or expression, then follow the order of operations​

​Function

​Graph of a Function