Exponential Graphs

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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 does the graph of an exponential function look like?

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The graph of an exponential function is a smooth curve that either increases or decreases rapidly, depending on the base 'b'. If b > 1, the graph rises steeply; if 0 < b < 1, it falls steeply.

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What is the base of an exponential function?

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

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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 point where the graph crosses the y-axis, which occurs at (0, a).

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

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Changing the base 'b' affects the steepness of the graph. A larger base results in a steeper increase, while a base between 0 and 1 results in a rapid decrease.

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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 for functions of the form f(x) = a * b^x.

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What is exponential growth?

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Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to rapid increases over time, often modeled by f(t) = a * e^(kt).

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What is exponential decay?

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Exponential decay occurs when a quantity decreases at a rate proportional to its current value, often modeled by f(t) = a * e^(-kt).

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How do you identify an exponential function from a table of values?

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An exponential function can be identified from a table of values if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by equal intervals.

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What is the difference between linear and exponential functions?

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Linear functions have a constant rate of change, resulting in a straight line graph, while exponential functions have a variable rate of change, resulting in a curve.