Linear vs Exponential Functions

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What is a linear function?

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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?

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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 (a positive number), and x is the exponent.

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

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A linear function will show a constant difference in the y-values as the x-values increase by the same amount. If the differences are not constant, it is not linear.

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

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An exponential function will show a constant ratio of the y-values as the x-values increase by the same amount. If the ratios are not constant, it is not exponential.

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What is the general form of a linear equation?

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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 general form of an exponential equation?

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The general form of an exponential equation is y = a * b^x, where a is a constant, b is the base, and x is the exponent.

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of y with respect to x. It indicates how much y changes for a one-unit increase in x.

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What does the base of an exponential function represent?

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The base of an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function. It determines how quickly the function increases or decreases.

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If a function doubles its output for every increase of 1 in the input, what type of function is it?

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It is an exponential function.

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If a function increases by a fixed amount for every increase of 1 in the input, what type of function is it?

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It is a linear function.