PH: L3.1 Exponential Functions and Their 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 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 of the function.

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What does it mean for an exponential function to grow?

Back

An exponential function grows when the base 'b' is greater than 1, resulting in values that increase rapidly as 'x' increases.

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What does it mean for an exponential function to decay?

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An exponential function decays when the base 'b' is between 0 and 1, resulting in values that decrease 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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How do you graph an exponential function?

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To graph an exponential function, plot the y-intercept, identify the growth or decay direction based on the base, and draw a smooth curve that approaches the x-axis but never touches it.

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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 y = 0, which the graph approaches but never reaches as x approaches negative infinity.

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What is the domain of an exponential function?

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The domain of an exponential function is all real numbers, represented as (-∞, ∞).

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What is the range of an exponential function?

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The range of an exponential function is all positive real numbers, represented as (0, ∞).

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

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Changing the base of an exponential function affects the steepness of the graph; a larger base results in a steeper curve.