Exponential Functions

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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 is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of the function when x = 0, which is f(0) = a(b^0) = a.

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CCSS.HSF-IF.C.7E

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How do you simplify the expression (3x^4)(5x^3)?

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To simplify, multiply the coefficients and add the exponents: (3*5)x^(4+3) = 15x^7.

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CCSS.HSA.APR.A.1

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What is the common ratio in an exponential function?

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The common ratio in an exponential function is the factor by which the function's value changes as x increases by 1, represented as b in f(x) = a(b^x).

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CCSS.HSF-IF.C.8B

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How do you find the common ratio from a table of values?

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To find the common ratio, divide any f(x) value by the previous f(x) value in the table.

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CCSS.HSF.BF.A.2

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What is the simplified form of 10x^-2?

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The simplified form is 10/(x^2) or 10x^2 when expressed with positive exponents.

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What does it mean for a function to be exponential?

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A function is exponential if it can be expressed in the form f(x) = a(b^x), where the variable x is in the exponent.

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How do you identify the base of an exponential function?

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The base of an exponential function is the number that is raised to the power of x, represented as 'b' in f(x) = a(b^x).

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What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(x) = a(b^x) where b > 1.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(x) = a(b^x) where 0 < b < 1.