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 of the exponential (a positive real number), and 'x' is the exponent.

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What are the characteristics of the graph of an exponential growth function?

Back

The graph of an exponential growth function rises rapidly as x increases, approaches the x-axis but never touches it (asymptote), and passes through the point (0, a).

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What are the characteristics of the graph of an exponential decay function?

Back

The graph of an exponential decay function decreases rapidly as x increases, approaches the x-axis but never touches it (asymptote), and passes through the point (0, a).

Front

How can you identify an exponential growth function from its equation?

Back

An exponential growth function has a base 'b' greater than 1 in the equation f(x) = a * b^x.

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How can you identify an exponential decay function from its equation?

Back

An exponential decay function has a base 'b' between 0 and 1 in the equation f(x) = a * b^x.

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What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is the line y = 0, which the graph approaches but never reaches.

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What does the base of an exponential function determine?

Back

The base of an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

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What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the point (0, a), where 'a' is the initial value.

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How do transformations affect the graph of an exponential function?

Back

Transformations such as vertical shifts, horizontal shifts, reflections, and stretches/compressions can change the position and shape of the graph of an exponential function.

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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 at a constant rate.