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 does the slope of a linear function represent?

Back

The slope 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 is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

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 as (a, 0) where a is the value of x when y = 0.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, y also increases. This is indicated by a positive slope.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as x increases, y decreases. This is indicated by a negative slope.

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 (-∞, ∞), unless restricted by the context.

Front

What is end behavior in the context of linear functions?

Back

End behavior describes how the values of y behave as x approaches positive or negative infinity.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) for two points (x1, y1) and (x2, y2).