Exploring Functions: Domain and Range Essentials

The video tutorial introduces functions, explaining the difference between relations and functions. It covers key vocabulary such as domain and range, and demonstrates how to identify functions using mapping diagrams, ordered pairs, tables, and graphs. The vertical line test is introduced as a quick method to determine if a graph represents a function. Examples are provided to illustrate these concepts, emphasizing that a function pairs each input with exactly one output.

What is the set of all inputs of a function called?

• Range

• Domain

• Dependent Variable

• Output

Which of the following is true about a function?

• Each input can map to multiple outputs.

• Each output maps to exactly one input.

• Each output maps to multiple inputs.

• Each input maps to exactly one output.

In a mapping diagram, what indicates that a relation is not a function?

• An input maps to exactly one output.

• An input maps to multiple outputs.

• An output maps to multiple inputs.

• All inputs map to the same output.

Which of the following ordered pairs indicates that a relation is not a function?

• (6, -2), (-5, 4), (8, 0), (3, 1)

• (3, -2), (0, 0), (6, 5), (8, 5)

• (3, -2), (0, 0), (6, 5), (3, 1)

• (6, -2), (-5, 4), (8, 0), (3, -2)

How can you tell if a table represents a function?

• All X values are different.

• Y values repeat.

• All Y values are different.

• X values repeat.

What happens to an input in a function machine?

• It produces no output.

• It remains unchanged.

• It produces exactly one output.

• It can produce multiple outputs.

If an input of 7 goes into a function machine that multiplies by 2, what is the output?

• 14

• 7

• 2

• 0

What does the vertical line test determine?

• If a graph is linear.

• If a graph is quadratic.

• If a graph represents a function.

• If a graph is continuous.

What indicates that a graph fails the vertical line test?

• A vertical line crosses the graph at exactly one point.

• A vertical line crosses the graph at multiple points.

• A horizontal line crosses the graph at exactly one point.

• A horizontal line crosses the graph at multiple points.

Which of the following graphs represents a function?

• A graph where a horizontal line crosses at one point.

• A graph where a horizontal line crosses at two points.

• A graph where a vertical line crosses at one point.

• A graph where a vertical line crosses at two points.