Identifying 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 form a straight line when graphed. Examples include quadratic functions, exponential functions, and absolute value functions.

Front

How can you identify a linear function from its equation?

Back

A linear function can be identified by its equation being in the form y = mx + b, where m and b are constants.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

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 y changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the graph intersects the y-axis, represented by the value of b in the equation y = mx + b.

Front

Give an example of a linear function.

Back

An example of a linear function is y = 3x + 2.

Front

Give an example of a nonlinear function.

Back

An example of a nonlinear function is y = x^2 + 1.

Front

What is the graph of a linear function like?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What is the graph of a quadratic function like?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards.