Characteristics of 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.

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What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of an exponential function is a horizontal line that the graph approaches as x approaches positive or negative infinity. For functions of the form f(x) = a * b^x, the horizontal asymptote is typically y = 0.

Tags

CCSS.HSF-IF.C.7E

Front

What is the range of an exponential function?

Back

The range of an exponential function f(x) = a * b^x (where a > 0) is (0, ∞) if the function approaches y = 0 as x approaches negative infinity.

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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 the graph crosses the y-axis, which occurs at (0, a).

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

An exponential function exhibits growth when the base 'b' is greater than 1, resulting in the function increasing rapidly as x increases.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

An exponential function exhibits decay when the base 'b' is between 0 and 1, resulting in the function decreasing rapidly as x increases.

Tags

CCSS.HSF-IF.C.8B

Front

What is the domain of an exponential function?

Back

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

Front

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

Back

Changing the base of an exponential function affects the rate of growth or decay. A larger base results in faster growth, while a smaller base (greater than 0 but less than 1) results in slower growth or decay.

Tags

CCSS.HSF-IF.C.7E

Front

What is the significance of the constant 'a' in an exponential function?

Back

The constant 'a' in an exponential function f(x) = a * b^x determines the initial value of the function when x = 0, which is also the y-intercept.

Tags

CCSS.HSF-IF.C.8B

Front

What is an example of an exponential growth function?

Back

An example of an exponential growth function is f(x) = 2 * 3^x, where the base 3 indicates rapid growth.

Tags

CCSS.HSF-LE.A.1A