Identifying Functions and Function Tables

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

Does the graph represent a function if it fails the vertical line test?

Back

No, if a graph fails the vertical line test, it does not represent a function.

Front

What does it mean for a mapping to be a function?

Back

A mapping is a function if each input is paired with exactly one output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

What does it mean if an x-value has two y-values in a relation?

Back

If an x-value has two y-values, the relation is not a function.

Front

What is a function table?

Back

A function table is a table that shows pairs of input and output values for a function.

Front

How can you determine if a relation is a function from a set of ordered pairs?

Back

Check if any x-value is repeated with different y-values; if so, it is not a function.