Describing Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and can include curves, parabolas, etc.

Front

What does it mean for a function to be proportional?

Back

A function is proportional if it can be expressed in the form y = kx, where k is a constant.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph to a straight line, while nonlinear functions have a variable rate of change and graph to curves.

Front

What is the standard form of a linear equation?

Back

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

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept?

Back

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

Front

What is a quadratic function?

Back

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

Front

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

Back

A linear function will have a constant difference in the y-values for equal increments in the x-values.