Functions, Domain & Range

What you'll learn

Determine whether a relation is a function
Identify the domain and range of a function
Represent functions with tables, graphs, and rules

Words to know

Relation —: any set of ordered pairs
Function —: a relation where each input has exactly one output
Domain —: the set of all input values
Range —: the set of all output values
Vertical line test —: a graph is a function if no vertical line crosses it twice

Why it matters Functions describe dependable relationships, like cost from quantity, where each input gives one clear output.

Worked examples

Model ItI do

Is the relation {(1, 2), (2, 4), (3, 6)} a function?

Check that no input repeats with a different output. The inputs 1, 2, 3 each appear once, so every input has exactly one output. Yes, it is a function.

Try It TogetherWe do

Give the domain and range of {(0, 5), (1, 7), (2, 9)}.

The domain is the set of inputs: {0, 1, 2}. The range is the set of outputs: {5, 7, 9}.

Now YouYou do

Is the relation {(1, 3), (1, 5), (2, 8)} a function?

Check whether any input is paired with more than one output. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

1.Is {(1, 2), (2, 4), (3, 6)} a function?
2.State the domain of {(2, 5), (4, 7), (6, 9)}.
3.What test tells whether a graph is a function?

On Level

The core Quick Check from the book.

1.Is {(2, 4), (3, 9), (4, 16)} a function?
2.State the domain of {(1, 2), (5, 6), (7, 8)}.
3.State the range of {(0, 1), (2, 1), (4, 1)}.
4.Is {(3, 1), (3, 2), (4, 5)} a function?
5.What test tells if a graph is a function?

Challenge

Stretch your thinking.

1.Is {(1, 4), (2, 5), (1, 6)} a function? Explain.
2.A function is given by the rule y = 3x with domain {0, 1, 2, 3}. List the range.
3.State the domain and range of {(-2, 4), (-1, 1), (0, 0), (1, 1)}.