Characteristics of Linear & Exponential Functions

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What is a linear function?

Back

A linear function is a function that graphs to a straight line. It 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

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What is an exponential function?

Back

An exponential function is a function of the form y = ab^x, where a is a constant, b is a positive real number, and x is the exponent. The graph of an exponential function increases or decreases rapidly.

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What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis. It is found by setting x = 0 in the function.

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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How do you find the y-intercept of a linear function?

Back

To find the y-intercept of a linear function, set x = 0 and solve for y.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of the function (y) also increases.

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What does it mean for a function to be decreasing?

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A function is decreasing if, as x increases, the value of the function (y) decreases.

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 a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Tags

CCSS.8.EE.B.5

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What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to faster growth over time.