Characteristics of 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 domain of a linear function?

Back

The domain of a linear function is all real numbers, represented as (-∞, ∞).

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, represented as (-∞, ∞).

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept of a linear function?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented as (0, b).

Front

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

Back

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

Front

What does it mean if a linear function has a positive slope?

Back

A positive slope indicates that as x increases, y also increases, resulting in an upward slant of the line.

Front

What does it mean if a linear function has a negative slope?

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

What is the significance of the x-intercept?

Back

The x-intercept is the value of x when y is zero; it indicates where the line crosses the x-axis.

Front

What is the significance of the y-intercept?

Back

The y-intercept is the value of y when x is zero; it indicates where the line crosses the y-axis.