Key feature of exponential functions

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What is an exponential function?

Back

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 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 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 f(0) = a.

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What is the range of an exponential function?

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The range of an exponential function is (0, ∞) if a > 0, or (-∞, 0) if a < 0.

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How does the base 'b' affect the graph of an exponential function?

Back

If b > 1, the function increases rapidly; if 0 < b < 1, the function decreases rapidly.

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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 that the graph approaches but never touches, typically y = 0.

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What happens to the value of an exponential function as x approaches infinity?

Back

As x approaches infinity, the value of an exponential function with a base greater than 1 approaches infinity.

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What happens to the value of an exponential function as x approaches negative infinity?

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As x approaches negative infinity, the value of an exponential function with a base greater than 1 approaches 0.

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What is the effect of changing the constant 'a' in an exponential function?

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Changing 'a' affects the vertical stretch or compression of the graph; if 'a' is positive, the graph is above the x-axis.

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What is an example of an exponential growth function?

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An example of an exponential growth function is f(x) = 2^x.