Characteristics of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation 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 in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you determine if a linear function is increasing or decreasing?

Back

If the slope (m) is positive, the function is increasing; if the slope is negative, the function is decreasing.

Front

What is the domain of a linear function?

Back

The domain of a linear function is the set of all possible x-values that can be input into the function.

Front

What is the range of a linear function?

Back

The range of a linear function is the set of all possible y-values that the function can output.

Front

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

Back

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

Front

What does it mean for a function to be positive?

Back

A function is positive when its output (y-value) is greater than zero for the given input (x-value).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.

Front

What is the difference between domain and range?

Back

Domain refers to all possible input values (x-values), while range refers to all possible output values (y-values) of a function.