Linear and Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and has a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and has a variable rate of change.

Front

What does it mean for a function to pass the vertical line test?

Back

A function passes the vertical line test if no vertical line intersects the graph at more than one point.

Front

What is the initial value in a function?

Back

The initial value is the y-value when x is zero, often representing the starting point of the function.

Front

What is the slope of a linear function?

Back

The slope is the rate of change of the function, calculated as the rise over run between two points on the line.

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) has exactly one output (y-value).

Front

What is the formula for a linear function?

Back

The formula for a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in y-values divided by the difference in x-values is the same for any two points.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form y = ax^2 + bx + c.

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, occurring when x = 0.