Characteristics of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form 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 (m) of a linear function represents the rate of change of the function, indicating 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 as (0, b) in the function f(x) = mx + b.

Front

What is the domain of a linear function?

Back

The domain of a linear function is the set of all possible input values (x-values) for which the function is defined, typically all real numbers.

Front

What is the range of a linear function?

Back

The range of a linear function is the set of all possible output values (y-values) that the function can produce, which is also typically all real numbers unless restricted.

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 end behavior of a linear function?

Back

The end behavior of a linear function describes how the function behaves as x approaches positive or negative infinity. For a positive slope, as x → ∞, f(x) → ∞ and as x → -∞, f(x) → -∞.

Front

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

Back

The rate of change indicates how steep the line is and the direction it moves. A positive rate of change means the function is increasing, while a negative rate indicates it is decreasing.

Front

What are parallel lines in the context of linear functions?

Back

Parallel lines are lines that have the same slope but different y-intercepts. They never intersect.

Front

What are perpendicular lines in the context of linear functions?

Back

Perpendicular lines are lines that intersect at a right angle. The slopes of two perpendicular lines are negative reciprocals of each other.