Functions

Front

What is the range of a relation?

Back

The range of a relation is the set of all output values (y-values) that correspond to the input values (x-values).

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line intersects the graph at most once (Vertical Line Test).

Front

What is the definition of a function?

Back

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

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input (x-value) is associated with more than one output (y-value).

Front

Given f(x)=2x+1, how do you find f(x) for a specific value of x?

Back

Substitute the specific value of x into the function and calculate the result.

Front

What is the output of the function f(x)=2x+1 when x=2?

Back

f(2) = 2(2) + 1 = 5.

Front

What is the significance of the x-value in a function?

Back

The x-value (input) determines the corresponding y-value (output) in a function.

Front

What is a vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line intersects the graph more than once.

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) = x^2, where each input x has a unique output x^2.