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 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 = ab^x, where a is a constant, b is the base, and x is the exponent.

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

Back

A linear function will have a constant rate of change, meaning the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

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

Back

An exponential function will have a constant ratio of change, meaning the ratio of consecutive y-values will be the same when the x-values increase by the same amount.

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What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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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 = ab^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 unit change 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.

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What is the y-intercept in a linear function?

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The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

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What is an example of a linear function in real life?

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An example of a linear function in real life is earning a fixed salary, where the total earnings increase by a constant amount over time.