Relations & Functions

Relations & Functions

​Dr. Tom Giles

What is a relation?

A relation is a set of inputs and outputs

• Ordered Pairs

• Table

• Graph

• Mapping Diagram

What is a function?

A function is a relation in which each input(domain - x) is paired with exactly one output(range -y)
x's Do Not Repeat

Function or Not a Function?

Which relation represents y as a function of x?

Which relation does not represent y as a function of x?

What is the difference between a Relation and a Function?

What is the difference between a Function and an Equation?

Identify the domain and range. Does the relation represent y as a function of x?

• Domain

• {-2, 0, 4, 5}

• Range

• {2, 5, 6}

• Is the relation a function?

• Yes; the x's DO NOT repeat

Identify the domain and range. Does the relation represent y as a function of x?

• Domain

• {-1, 2, 4}

• Range

• {3, 6, 8}

• Is the relation a function?

• No; the x value of -1 repeats

Multiple Choice

Identify the domain and range. Does the relation represent y as a function of x?

• D: {4}

  R: {1, 3, 7, 10}

  No, it is not a function.

• D: {1, 3, 7, 10}

  R: {4}

  Yes, it is a function

• D: {4}

  R: {1, 3, 7, 10}

  Yes, it is a function.

Multiple Choice

Which table represents y as a function of x?

• Table 1

• Table 2

Mapping Diagrams

Take a look at the 2 mapping diagrams on the next slide. Decide which mapping is a function and why.

Mapping Diagrams

A mapping is a function if there is only ONE ARROW coming out of each DOMAIN value. In the previous slide, Mapping #1 is a function and Mapping #2 is NOT a function.

x's DO NOT repeat

Multiple Choice

Which relation represents y as a function of x?

• Mapping #1

• Mapping #2

Graphs

Take a look at the 2 graphs on the next slide. Decide which graph is a function and why.

Use the Vertical Line Test to determine a function from a graph.

• If a vertical line can be drawn on the graph that intersects the graph more than once, the graph DOES NOT represent a Function.

Function Notation

• Easy Reference

• Displays the Input

Multiple Choice

If  $$f\left(x\right)=3x^2-4x+5$$ , which would calculate the value of  $$f\left(3\right)$$  ?

• $$3\left(3\right)^2-4\left(3\right)+5$$  

• $$3\left(3\right)^2-4+5$$  

• $$3^2-4\left(3\right)+5$$  

Multiple Choice

Which graph does not represent y as a function of x?

• Graph #1

• Graph #2