Graphing 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 a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase as time progresses.

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

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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 as time progresses.

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What is the base in an exponential function?

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

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What is an asymptote in the context of 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 typically the x-axis (y=0).

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How can you identify exponential growth on a graph?

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

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How can you identify exponential decay on a graph?

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

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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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What is the significance of the y-intercept in 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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What is the difference between exponential functions and linear functions?

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Exponential functions grow or decay at a rate proportional to their current value, while linear functions grow or decay at a constant rate.