Domain and Range of Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the vertical line test?

Back

The vertical line test is a method used 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 following set represent a function? {(1,2), (1,3), (2,4)}

Back

No, because the input value '1' is associated with two different output values (2 and 3).

Front

What is an example of a function?

Back

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

Front

What does it mean if a function is not defined for a certain x-value?

Back

It means that there is no corresponding y-value for that x-value in the function.

Front

How do you find the domain of a function given a graph?

Back

To find the domain from a graph, identify all the x-values that the graph covers.

Front

How do you find the range of a function given a graph?

Back

To find the range from a graph, identify all the y-values that the graph covers.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2, because the function is undefined at that point.