Identifying Linear 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, represented by the equation 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

How can you identify a function from a set of points?

Back

A set of points represents a function if no two points have the same x-coordinate.

Front

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function, indicating how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output.

Front

What does it mean if a graph is not a function?

Back

A graph is not a function if any vertical line drawn intersects the graph at more than one point.

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 integers.

Front

What is a vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if a vertical line crosses the graph more than once, it is not a function.