Exponential vs Linear Functions!

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What is a linear function?

Back

A linear function is a function that creates a straight line when graphed. 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.

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What is an exponential function?

Back

An exponential function is a function in which an independent variable is 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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What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in the y-values divided by the difference in the x-values is the same for any two points on the function.

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

Back

A linear function can be identified from a table of values if the differences between consecutive y-values are constant as the x-values increase.

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How can you identify an exponential function from a table of values?

Back

An exponential function can be identified from a table of values if the ratio of consecutive y-values is constant as the x-values increase.

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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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What is the difference between linear and exponential growth?

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Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

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What is the slope of a linear function?

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The slope of a linear function is the ratio of the change in y to the change in x, representing the steepness of the line.

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What does it mean for a function to be neither linear nor exponential?

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A function is neither linear nor exponential if it does not fit the characteristics of either type, such as having a variable rate of change or a non-constant pattern.

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What is an example of a linear function?

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