STAAR review Exponential Functions

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent.

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What does exponential growth mean?

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Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase.

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What does exponential decay mean?

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Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a(b^x).

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How do you identify exponential growth from a graph?

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Exponential growth is identified by a curve that rises steeply to the right, indicating that the function's value increases rapidly as x increases.

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How do you identify exponential decay from a graph?

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Exponential decay is identified by a curve that falls steeply to the right, indicating that the function's value decreases rapidly as x increases.

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What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(x) = a(1 + r)^x, where 'r' is the growth rate.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(x) = a(1 - r)^x, where 'r' is the decay rate.

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What is the domain of an exponential function?

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The domain of an exponential function is all real numbers, represented as (-∞, ∞).

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What is the range of an exponential growth function?

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The range of an exponential growth function is (0, ∞), meaning it can take any positive value.