Graphing Exponential Functions

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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.

Front

What is the general form of an increasing exponential function?

Back

An increasing exponential function has a base greater than 1, typically expressed as f(x) = a(b^x) where b > 1.

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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 where x = 0, which is (0, a).

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How do you determine the y-intercept of the function y = 3^x?

Back

To find the y-intercept, substitute x = 0: y = 3^0 = 1, so the y-intercept is (0, 1).

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What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What is the horizontal asymptote of the function f(x) = 2(3^x)?

Back

The horizontal asymptote is y = 0.

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What type of function is f(x) = 2^x?

Back

f(x) = 2^x is an example of an exponential growth function.

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What is the horizontal asymptote of the function f(x) = 13(0.5^x)?

Back

The horizontal asymptote is y = 0.

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What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the base of the exponential function is between 0 and 1, causing the function to decrease as x increases.

Front

What is the base of the exponential function in y = 50(1.4^x)?

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The base of the exponential function is 1.4.