Solving & Graphing Exponential Equations

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What is an exponential equation?

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Set the exponents equal: -2n = 6. Solve for n: n = -3.

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The range is (-8, ∞). The graph approaches y = -8 but never touches it.

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How do you rewrite the number 8 as a power of 2?

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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. For exponential functions, the horizontal asymptote is often y = 0.

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What is the base of an exponential function?

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How do you graph an exponential function?

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Start by plotting points for various x values, then draw a smooth curve that approaches the asymptote.

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What does it mean for an exponential function to be increasing?

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An exponential function is increasing if its base is greater than 1, meaning as x increases, f(x) also increases.

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What does it mean for an exponential function to be decreasing?

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An exponential function is decreasing if its base is between 0 and 1, meaning as x increases, f(x) decreases.