Writing and Interpreting Exponential Functions STAAR Review

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What is an exponential function?

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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.

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

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The graph of an exponential function is a smooth curve that either increases or decreases rapidly. It has a horizontal asymptote, typically the x-axis, and does not intersect it.

Tags

CCSS.HSF-IF.C.7E

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How do you identify the base of an exponential function from its equation?

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In the equation f(x) = a * b^x, the base 'b' is the number that is raised to the power of 'x'. It is the coefficient of the exponential term.

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CCSS.HSF-IF.C.8B

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What is the difference between exponential growth and exponential decay?

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

Tags

CCSS.HSF-IF.C.8B

Front

What is the formula for exponential growth?

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The formula for exponential growth is f(t) = a * e^(kt), where 'a' is the initial amount, 'e' is Euler's number (approximately 2.718), 'k' is the growth rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

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What is the formula for exponential decay?

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The formula for exponential decay is f(t) = a * e^(-kt), where 'a' is the initial amount, 'e' is Euler's number, 'k' is the decay rate, and 't' is time.

Tags

CCSS.HSF-LE.A.1A

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How do you convert an exponential function to logarithmic form?

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To convert an exponential function of the form b^y = x to logarithmic form, you write it as log_b(x) = y.

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CCSS.HSF.BF.B.5

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What is the inverse of an exponential function?

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The inverse of an exponential function is a logarithmic function. If f(x) = b^x, then its inverse is f^(-1)(x) = log_b(x).

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CCSS.HSF-BF.B.4A

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What is the domain and range of an exponential function?

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The domain of an exponential function is all real numbers (-∞, ∞), and the range is all positive real numbers (0, ∞).

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How do you find the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a * b^x is found by evaluating f(0), which equals a, since b^0 = 1.

Tags

CCSS.HSF-IF.C.7E