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, meaning it adds or subtracts the same value for each unit increase in x.

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What is an exponential function?

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An exponential function is a function where the output is multiplied by a constant factor for each unit increase in the input. It grows or decays at a rate proportional to its current value.

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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 as the x-values increase by the same amount.

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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 as the x-values increase by the same amount.

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What is the general form of a linear function?

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The general form of a linear function 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 function?

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The general form of an exponential function is y = ab^x, where a is a constant, b is the base (growth factor), and x is the exponent.

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What does it mean for a function to have a constant rate of change?

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A constant rate of change means that for every unit increase in x, the change in y is always the same, characteristic of linear functions.

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What does it mean for a function to have a variable rate of change?

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A variable rate of change means that the change in y is not constant and can increase or decrease at different rates, characteristic of exponential functions.

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

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An example is the relationship between the number of hours worked and the amount of money earned at a constant hourly wage.

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

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An example is population growth, where the population increases by a percentage of the current population each year.