Functions, Domain & Range, Function Notation

Functions, Domain & Range, Function Notation

By Shalynne Orth

(3, 2) (3, 5) (4, 6) ( 7, 8)

This is NOT a function because the x value 3 repeats

Multiple Choice

Is this set of ordered pairs a function or not a function? 

• Function
• Not a Function 

Multiple Choice

Is this set of ordered pairs a function or not a function?

• Function

• Not a Function

• NOT A FUNCTION

• X values repeat

Multiple Choice

• Function
• Not a Function

Multiple Choice

Which value shown can replace the letter, a, so that the table is NOT a function?

• -11
• -1
• 25
• 3

• FUNCTION

• Each x has only 1 y value

Multiple Choice

Is this mapping a function or not a function? 

• Function
• Not a Function

• FUNCTION

• Passes the vertical line test

• NOT A FUNCTION

• connects vertically, so it fails the vertical line test

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 this a function? Explain.

• Yes; each x-value has one corresponding y-value.
• No; it is not a straight line.
• Yes; it passes the vertical line test.
• No; there is a line connecting the dots.

Multiple Select

Check all the boxes that represpent Domain

• Input

• Output

• X values

• How far left, how far right

• Independent Variable

Multiple Choice

What is the domain?

• {-4, -1, 0, 2, 7}
• {-5, -4, -1, 0, 1, 2, 4, 7}
• {-5, 0, 1, 2, 4}
• {5}

Multiple Choice

What is the Domain?

• {-3, -1, 1, 3, 5, 7, 9}
• {-3, -2, -1, 0, 1, 2, 3}
• -3 ≤ x ≤ 3
• -3 ≤ x ≤ 9

Domain

• When it comes to domain think how far left, and how far right.

  
  

    

• Remember the X-axis goes left to right.

  
  

• If the dot is open, then you use these inequalities <,>.

  
  

    

• If the dot is closed or shaded, then you use these inequalities ≤,≥

    

Multiple Choice

What is the Domain?

• -3 ≤ x < 5
• -3 ≤ y < 5
• -8 ≤ x < 5
• -8 ≤ y < 5

Range

• When it comes to range, it is the y variable

• It can also be called the output

• You may also see it called the dependent variable

• When trying to figure out the range, figure out how far up and how far down

Multiple Choice

Which is the set of all y-values or the outputs?

• Domain

• Range

• Relation

• Function

Multiple Choice

For the function (0,1), (1,-3), (2,-4), & (-4,1), which choice gives the correct domain & range?

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

Multiple Choice

What is the Range of this function?

• -6 ≤ y ≤ 6
• 0 ≤ y ≤ 6
• No Solution
• 4 ≤ y ≤ 3

Multiple Choice

What is the range?

• {-3, -1, 2, 4}
• {0, 4, 7} 
• {0, 4, 4, 7}
• {7, 4, 0}

Multiple Choice

What is the range?

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

Describing Real World Graphs

Multiple Choice

Multiple Choice

Multiple Choice

Functions can be represented by equations, too!

​The equation helps us find points in the domain and range of the function.

​

Let's practice this on the next few slides.​

​

Fill in the Blanks

Fill in the table.

A=

Fill in the Blanks

Fill in the table.

B=

Fill in the Blanks

Fill in the table.

C=

Fill in the Blanks

Fill in the table.

D=

Fill in the Blanks

What is the slope?

Write your answer as an integer.

m=

Fill in the Blanks

What is the y=intercept?

b=

Multiple Choice

Which is the graph of the function $$y=-4x+3$$ ?

• Blue

• Red

• Purple

• Green

Function Notation

"F of x" means the function labeled "f" has an input of "x". It does NOT mean "f times x."

Function notation is just a specific way of writing an equation.

y = 3x + 4 is the SAME as f(x) = 3x + 4

Multiple Choice

If a question asks you to find f(2), what does that mean?

• Let x = 2

• Let y = 2

Multiple Choice

If f(x) = 2x+1, what would the function look like once you substitute in a 1 to find f(1)?

• f(x) = 21+1

• f(1) = 2 (1) + 1

• f(1) = 2x (1) + 1

Multiple Choice

If I know that f(2) = 4, what is another way I can write my answer?

• (4,2)

• (2, 4)

• That is the only way to write it.

Multiple Choice

If f(x) = -3x - 8, find f(-1).

• f(-1) = 5

• f(-1) = -5

• f(-1) = -12

• f(-1) = -10

Multiple Choice

g(x) = 3x + 1

g(2) = _______

• 6

• 7

• 8

• 9

Multiple Choice

If f(x) = x - 5, what is the value of x when f(x) = 15?

• 20

• 10

• 5

• 0