Key Features of Functions Review - Stewart

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 the point where the function crosses the y-axis (x=0).

Front

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

Back

To find the x-intercept, set y=0 in the function and solve for x.

Front

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

Back

To find the y-intercept, set x=0 in the function and solve for y.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the function's value also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the function's value decreases.

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

What is the significance of the domain and range in a function?

Back

The domain and range provide information about the possible inputs and outputs of the function, which is essential for understanding its behavior.

Front

How can you determine if a function is increasing or decreasing from its graph?

Back

By observing the slope of the graph: if the graph rises as you move from left to right, it is increasing; if it falls, it is decreasing.

Front

What is a function's intercept form?

Back

Intercept form expresses a function in terms of its x- and y-intercepts, typically written as f(x) = a(x - x1)(x - x2) + y-intercept.