Exponential Functions (Graphs)

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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 the graph of an exponential growth function look like?

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The graph of an exponential growth function rises steeply as x increases, starting from a point above the x-axis and approaching the y-axis but never touching it.

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What does the graph of an exponential decay function look like?

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The graph of an exponential decay function decreases rapidly as x increases, starting from a point above the x-axis and approaching the x-axis but never touching it.

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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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How can you identify exponential growth from a graph?

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Exponential growth can be identified by a curve that rises steeply to the right, indicating that the function's value increases rapidly as x increases.

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How can you identify exponential decay from a graph?

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Exponential decay can be identified by a curve that falls steeply to the right, indicating that the function's value decreases rapidly as x increases.

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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 decay function?

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The horizontal asymptote of an exponential decay function is the x-axis (y=0), which the graph approaches but never reaches.

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What is the horizontal asymptote of an exponential growth function?

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The horizontal asymptote of an exponential growth function is also the x-axis (y=0), which the graph approaches 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 base between 0 and 1 results in decay.