Linear vs. Nonlinear

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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.

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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. It can include curves, parabolas, and other shapes that do not have a constant rate of change.

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CCSS.8.F.A.3

Front

How can you identify a linear function from its graph?

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

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What are the characteristics of a linear equation?

Back

Linear equations have a degree of 1, can be written in the form Ax + By = C, and their graph is a straight line.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What are some examples of linear functions?

Back

Examples of linear functions include f(x) = 2x + 3, f(x) = -x + 5, and f(x) = 0.5x.

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CCSS.HSF.LE.A.2

CCSS.8.F.B.4

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include f(x) = x^2, f(x) = sin(x), and f(x) = e^x.

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CCSS.8.F.A.3

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line.

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CCSS.8.EE.B.5

Front

What does it mean for a function to be quadratic?

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A quadratic function is a type of nonlinear function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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How does the graph of a quadratic function differ from a linear function?

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The graph of a quadratic function is a parabola, which can open upwards or downwards, while the graph of a linear function is a straight line.

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CCSS.HSF-IF.C.7A

Front

What is the significance of the y-intercept in a linear function?

Back

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