Linear, Non-Linear, or Not a Function?

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line. Its graph can be a curve, a circle, or any other shape that is not a straight line.

Front

What does it mean for a relation to not be a function?

Back

A relation is not a function if at least one input (x-value) corresponds to more than one output (y-value).

Front

How can you identify a linear function from a graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

Front

How can you identify a non-linear function from a graph?

Back

A non-linear function can be identified by its curved graph, which does not have a constant slope.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change of y with respect to x, represented by 'm' in the equation y = mx + b.

Front

What is the y-intercept of a linear function?

Back

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

Front

Can a vertical line be a function?

Back

No, a vertical line cannot be a function because it fails the vertical line test; it has multiple y-values for a single x-value.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3, which graphs to a straight line.