Graphs of Exponential Functions Review

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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 does the graph of an exponential function look like?

Back

The graph of an exponential function is a smooth curve that either increases or decreases rapidly, depending on whether the base 'b' is greater than 1 (increasing) or between 0 and 1 (decreasing).

Front

What is the base of an exponential function?

Back

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.

Front

What happens to the graph of an exponential function as x approaches infinity?

Back

As x approaches infinity, the graph of an exponential function with a base greater than 1 will rise towards infinity, while a base between 0 and 1 will approach zero.

Front

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 f(0) = a.

Front

How do you find the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is typically y = 0, which the graph approaches but never touches as x approaches negative infinity.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in value. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in value.

Front

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

Back

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 the same amount.

Front

What is the domain of an exponential function?

Back

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

Front

What is the range of an exponential function?

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The range of an exponential function is (0, ∞) for growth functions and (−∞, 0) for decay functions.