Linear and Nonlinear 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Examples include quadratic functions, exponential functions, and others.

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 equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

In the equation y = 8x + 6, what is the initial value?

Back

The initial value is 6, which is the y-intercept.

Front

In the equation y = x^2 + 7, is the function linear or nonlinear?

Back

The function is nonlinear because it includes a squared term.

Front

What is the rate of change in a situation where a fitness club opens with 80 members and increases by 15 members each month?

Back

The rate of change is 15 members per month.

Front

How can you identify a linear function from its equation?

Back

A linear function will have no exponents greater than 1 and can be written in the form y = mx + b.

Front

What is the general form of a linear equation?

Back

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

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as x increases, y also increases.