Linear vs NonLinear Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

How can you tell if a relation is a function using a table?

Back

A relation is not a function if any x-value is paired with more than one y-value.

Front

What does it mean if an x-value is repeated in a function?

Back

If an x-value is repeated with different y-values, the relation is not a function.

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 may include curves or other shapes.

Front

How can you identify a linear function from a graph?

Back

A linear function will show a straight line when graphed.

Front

How can you identify a nonlinear function from a graph?

Back

A nonlinear function will show a curve or any shape that is not a straight line when graphed.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the relation is not a function.

Front

What is the slope of a linear function?

Back

The slope is the rate of change of the function, representing how much y changes for a change in x.

Front

What does the y-intercept represent in a linear function?

Back

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