Transformations of Functions

Front

What are the x- and y-intercepts of a function?

Back

The x-intercept is the point where the function crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

How do you determine where a function is increasing or decreasing?

Back

A function is increasing on intervals where the output values rise as the input values increase, and decreasing where the output values fall.

Front

What is the domain of a function?

Back

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

Front

How do you find the intervals where a function is positive or negative?

Back

A function is positive where its output values are greater than zero and negative where its output values are less than zero.

Front

What does it mean for a function to be increasing on an interval?

Back

It means that as x increases, the value of the function f(x) also increases.

Front

What does it mean for a function to be decreasing on an interval?

Back

It means that as x increases, the value of the function f(x) decreases.

Front

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

Back

The x-intercept indicates the value of x where the function's output is zero.

Front

What is the significance of the y-intercept in a function?

Back

The y-intercept indicates the value of y where the function's input is zero.

Front

How can you identify the domain of a function from its graph?

Back

The domain can be identified by observing the x-values for which the graph exists.