Characteristics of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation f(x) = mx + b.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, as the output can take any value depending on the input.

Front

How do you determine if a function is linear?

Back

A function is linear if it can be expressed in the form f(x) = mx + b, where m and b are constants.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, f(x) also increases. For linear functions, this occurs when the slope (m) is positive.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, f(x) decreases. For linear functions, this occurs when the slope (m) is negative.

Front

What is a horizontal line in terms of a linear function?

Back

A horizontal line is a linear function with a slope of 0, represented by the equation f(x) = b, where b is a constant.

Front

What is a vertical line in terms of a function?

Back

A vertical line is not a function because it does not pass the vertical line test; it has an undefined slope.