Linear and Nonlinear Functions

Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 is the definition of a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed. Its rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line drawn through the graph intersects it at most once. This is known as the vertical line test.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a function. If any vertical line intersects the curve more than once, then the curve is not a function.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as the input values increase, the output values decrease.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it has the form f(x) = c, where c is a constant.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input variable.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values in a table. This means that the difference in y-values divided by the difference in x-values will be the same for any two points.