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 a constant rate of change and can be expressed in the form y = 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 create a straight line when graphed. The rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

Tags

CCSS.8.F.A.3

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the y-values for equal differences in the x-values. This means the ratio of the change in y to the change in x is constant.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How can you identify a nonlinear function from a table of values?

Back

A nonlinear function will show varying differences in the y-values for equal differences in the x-values, meaning the ratio of the change in y to the change in x is not constant.

Tags

CCSS.8.F.A.3

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function. It indicates how much the y-value changes for a unit change in the x-value.

Tags

CCSS.8.EE.B.5

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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. It is the value of y when x is 0.

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What is an example of a linear function?

Back

An example of a linear function is y = 2x + 3. This function has a constant slope of 2 and a y-intercept of 3.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2. This function creates a parabolic curve when graphed.

Tags

CCSS.8.F.A.3

Front

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

Back

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

Tags

CCSS.8.F.A.1

Front

What is the significance of a constant ratio in a linear function?

Back

A constant ratio in a linear function indicates that the relationship between x and y is proportional, leading to a straight line when graphed.

Tags

CCSS.8.EE.B.5