Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = 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/run).

Front

How do you determine if a function is linear or nonlinear?

Back

A function is linear if it can be represented by a straight line on a graph. If the graph curves or has a variable slope, it is nonlinear.

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 does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is the y-intercept of a linear function?

Back

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

Front

What is the x-intercept of a linear function?

Back

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

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, use the formula (y2 - y1) / (x2 - x1) using two points from the table.