AP Precalculus Exponential Functions Review

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

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What is the base of an exponential function?

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The base of an exponential function is the constant 'b' in the function f(x) = a * b^x. It determines the rate of growth or decay.

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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 * b^x, where b > 1.

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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 * b^x, where 0 < b < 1.

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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 as x increases, indicating that the function's value increases rapidly.

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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 as x increases, indicating that the function's value decreases rapidly.

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What is the y-intercept of an exponential function?

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

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What is the horizontal asymptote of an exponential function?

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The horizontal asymptote of an exponential function is the line y = 0, which the graph approaches but never touches as x approaches negative infinity.

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What is the effect of changing the base 'b' in an exponential function?

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Changing the base 'b' affects the rate of growth or decay; a larger base results in faster growth, while a smaller base (greater than 1) results in slower growth.

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What is the inverse of an exponential function?

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The inverse of an exponential function is a logarithmic function, expressed as f^-1(x) = log_b(x/a).