Linear vs Nonlinear functions

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What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be curved or have various shapes, and it does not have a constant rate of change.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope and does not curve.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the rise (change in y) to the run (change in x) between any two points on the line.

Tags

CCSS.8.EE.B.5

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

Back

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

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What is the vertical line test?

Back

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

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Can a linear function have a slope of zero?

Back

Yes, a linear function can have a slope of zero, which means it is a horizontal line and the output value (y) remains constant regardless of the input value (x).

Tags

CCSS.8.EE.B.5

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which produces a parabolic graph.

Tags

CCSS.8.F.A.3

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What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x) is associated with exactly one output (y). A relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

Front

How do you determine if a graph is a function?

Back

To determine if a graph is a function, use the vertical line test. If any vertical line crosses the graph more than once, it is not a function.