Comparing Linear and 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 f(x) = 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 f(x) = a(b^x), where a is a constant, b is the base, and x is the exponent.

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What is the rate of change in a linear function?

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The rate of change in a linear function is constant, meaning it remains the same regardless of the value of x.

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What is the rate of change in an exponential function?

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The rate of change in an exponential function is not constant; it increases or decreases at an increasing rate as x changes.

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How can 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 for equal intervals of x-values.

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How can 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 for equal intervals of x-values.

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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 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 f(x) = a(b^x), where a is a constant and b is the base.

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Give an example of a real-world situation modeled by a linear function.

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An example is a taxi fare that charges a base fee plus a per-mile charge.

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Give an example of a real-world situation modeled by an exponential function.

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An example is population growth, where the population increases by a percentage over time.