Key Features of Functions

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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

How do you find the x-intercepts of a function?

Back

To find the x-intercepts, set the function equal to zero and solve for x.

Front

How do you find the y-intercept of a function?

Back

To find the y-intercept, evaluate the function at x = 0.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points in that interval, the function value at the second point is greater than at the first.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points in that interval, the function value at the second point is less than at the first.

Front

What is end behavior of a function?

Back

End behavior describes how the values of a function behave as the input approaches positive or negative infinity.

Front

What is a vertical stretch of a function?

Back

A vertical stretch occurs when the output values of a function are multiplied by a factor greater than 1, making the graph taller.

Front

What is a vertical compression of a function?

Back

A vertical compression occurs when the output values of a function are multiplied by a factor between 0 and 1, making the graph shorter.

Front

What does it mean to shift a function to the right?

Back

Shifting a function to the right means adding a positive value to the input (x) of the function.