Characteristics of Linear Functions

Front

What is a linear function?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

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. It is represented as (0, b) in the function f(x) = mx + b.

Front

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

Back

To find the x-intercept, set f(x) = 0 and solve for x. The x-intercept is the point where the graph crosses the x-axis.

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 it mean for a function to be positive?

Back

A function is positive when its output values (f(x)) are greater than zero. This occurs in the intervals where the graph is above the x-axis.

Tags

CCSS.HSF.LE.B.5

Front

What is the significance of the rate of change in a linear function?

Back

The rate of change is the same as the slope and indicates how steep the line is. It shows how much y changes for a given change in x.

Tags

CCSS.HSF-LE.A.1B

Front

What happens to the function as x approaches infinity?

Back

As x approaches infinity, the behavior of the function depends on the slope. If the slope is positive, f(x) approaches infinity; if negative, f(x) approaches negative infinity.

Front

What is a horizontal line in the context of linear functions?

Back

A horizontal line represents a linear function with a slope of 0. It has the form f(x) = b, where b is a constant.