Linear, Nonlinear, Function, Not a Function

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 is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its graph can be a curve, a circle, or any other shape that is not linear.

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

Front

What does it mean for a graph to be a function?

Back

A graph is a function if every input (x-value) has exactly one output (y-value). This means that no vertical line can intersect the graph at more than one point.

Front

What is the vertical line test?

Back

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

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear. It is either one or the other based on its graph.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which graphs to a straight line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which graphs to a parabola.