Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of the function when x = 0.

Front

How can you determine if a table of values represents a function?

Back

A table represents a function if each input (x-value) is associated with exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

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 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 difference between linear and nonlinear functions?

Back

Linear functions produce a straight line when graphed, while nonlinear functions produce curves or other shapes.

Front

What is a function notation?

Back

Function notation is a way to represent functions using symbols, typically written as f(x), where f is the function name and x is the input variable.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values (x) increase, the output values (y) also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values (x) increase, the output values (y) decrease.