Linear vs Non-Linear 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 y = 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 non-linear function?

Back

A non-linear function is a function that does not form a straight line when graphed. It can include quadratic, exponential, and other types of functions.

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CCSS.8.F.A.3

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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CCSS.8.EE.B.5

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

Back

The y-intercept (b) is the point where the line crosses the y-axis, indicating the value of y when x is 0.

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CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Give an example of a linear function.

Back

An example of a linear function is y = 3x + 2.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of a non-linear function.

Back

An example of a non-linear function is y = x^2.

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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.

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

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

Back

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

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CCSS.8.F.A.3

Front

What is the difference between a function and a non-function?

Back

A function assigns exactly one output for each input, while a non-function may assign multiple outputs for a single input.

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CCSS.8.F.A.1