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 a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

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What does the y-intercept of a function represent?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis. It is found by evaluating the function at x=0.

Front

What is the general form of an increasing exponential function?

Back

An increasing exponential function has the form f(x) = a(b^x) where 'b' > 1.

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What is the general form of a decreasing exponential function?

Back

A decreasing exponential function has the form f(x) = a(b^x) where '0 < b < 1.

Front

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

Back

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

Front

What is the horizontal asymptote of an exponential decay function?

Back

The horizontal asymptote of an exponential decay function is typically y=0, meaning the function approaches but never reaches this line.

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What is the domain of the function y=2^x?

Back

The domain of the function y=2^x is all real numbers: -∞ < x < ∞.

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What is the range of the function y=2^x?

Back

The range of the function y=2^x is all positive real numbers: y > 0.

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

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, resulting in a rapid increase over time.

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

Back

Exponential decay occurs when a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease over time.