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

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What does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when the growth rate of a function is proportional to its current value, leading to an increase that accelerates over time.

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What does it mean for a function to exhibit exponential decay?

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Exponential decay occurs when the value of a function decreases at a rate proportional to its current value, leading to a rapid decrease over time.

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In the function f(x) = 2(1.25)^x, what type of function is it?

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Exponential Growth.

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What is the domain of a function?

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The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

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The range of a function is the set of all possible output values (y-values) that the function can produce.

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What is an asymptote in relation to exponential functions?

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An asymptote is a line that a graph approaches but never touches. In exponential functions, the horizontal asymptote is often the line y = 0.

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What is the initial value in an exponential function?

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The initial value is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b^x).

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How do you identify the growth factor in an exponential function?

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The growth factor is the base 'b' in the function f(x) = a(b^x). If b > 1, the function exhibits growth.

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How do you identify the decay factor in an exponential function?

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The decay factor is the base 'b' in the function f(x) = a(b^x). If 0 < b < 1, the function exhibits decay.