Identifying Functions, Domain & Range

Identifying Functions & Domain and Range

By Nicole Chandler

Graphing

WARM UP/REVIEW:

Graph the following points:

$$A(2,-4)\ B(-2,3)\ C(0,6)\ D(-6,0)$$

Understand the concept of a function.

Learning Target: 

• I can determine whether a relation is a function.

• I can find the domain and range of a function.

Success Criteria: 

What are we learning today?

Think about the meanings of the compound words input and output by analyzing their prefixes and the root word put.

WORDS AND MATH

...pairs inputs (x values) with outputs (y values). "Cause and Effect"

For example, the number of hours you work and the pay you receive form a relation. The inputs are the hours worked, and the outputs are the pay amounts. Can you think of other relations?

Relation

VOCAB

Order doesn't actually matter, but often you'll see least to greatest.

In math, a function is a type of relation that pairs each input with exactly one output.

Multiple Choice

Determining Whether Relations Are Functions

Is the relation a function?

$$\left(-2,\ 2\right)\ \left(-1,\ 2\right)\ \left(0,\ 2\right)\ \left(1,\ 0\right)\ \left(2,0\right)$$

• YES

• NO

Multiple Choice

Determining Whether Relations Are Functions

Is the relation a function?

$$(4,0)\ (8,7)\ (6,4)\ (4,3)\ (5,2)$$

• YES

• NO

Multiple Choice

Determining Whether Relations Are Functions

Is the relation a function?

• YES

• NO

Multiple Choice

Determining Whether Relations Are Functions

Is the relation a function?

• YES

• NO

​Pro tip: Use your pencil and run it vertically (up and down) across the line. If it never passes through 2 points at the same time, it's a function!

Functions when graphing

Multiple Choice

Is the relation a function?

• YES

• NO

Multiple Choice

Is the relation a function?

• YES

• NO

Multiple Choice

Is the relation a function?

• YES

• NO

Multiple Choice

Is the relation a function?

• YES

• NO

Multiple Choice

Is the relation a function?

• YES

• NO

Multiple Choice

Is the relation a function?

• YES

• NO

Multiple Choice

Is the relation a function?

• YES

• NO

Open Ended

  Explain why you can use vertical lines to determine whether a graph represents a function.

Domain & Range of a Function

D = {-3, -1, 1, 4, 5}​

Order doesn't actually matter, but often you'll see least to greatest.

Domain is the set of X values

R = {-5, 0, 2, 6}

​

Don't repeat the 2​

​

Range is the set of Y values

Domain (X) = {-1, 0, 1, 2, 3}

​

Range (Y) = {1, 2, 3}​

​

​Can't remember which is which? D and R are alphabetical order and so are X and Y.

Multiple Choice

Which of these sets is the RANGE of the graph?

• {0, 6, 12, 18}

• {-2, 0, 2, 4}

• {-2, 2, 4}

• {6, 12, 18}

Multiple Choice

Which number is not an element of the domain?

• 2

• 1

• 0

• 6

Fill in the Blanks

What is the domain when the range is 3?

Multiple Choice

What is the domain?

• {0, 1, 2, 15}

• (0, 1, 2, 3}

• {3, 7, 11, 15}

• {3, 7, 11, 3}

Multiple Choice

What variable typically represents the domain?

• x

• y

Multiple Choice

What variable typically represents the range?

• x

• y

Multiple Choice

What is the domain?

• {5, 10, 15}

• {(5,2), (5,4), (10,6), (15,8)}

• {2, 4, 6, 8}

• {5, 2, 4, 10, 15}

Multiple Choice

What is the range of the mapping?

• {1, 2, 4}

• {0, 1, 2, 3}

• {0, 3}

• {1, 4}

Multiple Choice

Identify the domain of the following relation:
Remember domain is the "x" values

• -6, 14, 2, 28
• (-6,14), (0,32), (2,38), (4,44)
• -6, 0, 2, 4
• 14, 32, 38, 44

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