Linear vs Exponential

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What is a linear function?

Back

A linear function is a mathematical function that creates a straight line when graphed. It can be expressed in 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

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What is an exponential function?

Back

An exponential function is a mathematical function in which an independent variable appears in the exponent. It can be expressed in the form y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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How does a linear function grow?

Back

A linear function grows at a constant rate. This means that for every unit increase in x, y increases by a fixed amount.

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CCSS.HSF-LE.A.1B

Front

How does an exponential function grow?

Back

An exponential function grows at an increasing rate. This means that as x increases, y increases by a larger and larger amount.

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CCSS.HSF-IF.C.8B

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What is the general shape of a linear graph?

Back

The graph of a linear function is a straight line.

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CCSS.HSF-IF.C.7A

Front

What is the general shape of an exponential graph?

Back

The graph of an exponential function is a curve that rises rapidly, often starting slowly and then increasing steeply.

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CCSS.HSF-IF.C.7E

Front

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, represented by the value of b in the equation y = mx + b.

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What is the base in an exponential function?

Back

The base in an exponential function is the constant b in the equation y = a * b^x, which determines the rate of growth.

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CCSS.HSF-IF.C.8B

Front

Give an example of a linear function.

Back

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

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CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

Give an example of an exponential function.

Back

An example of an exponential function is y = 3 * 2^x.