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A function of x is a relation in which no two ordered pairs have the same x-value. x f(x) Does the information given define a function ? a 1 b 4 c 4 d 3 x f(x) a 1 b 2 c 3 d 4 a 5 1 6 2 5 1 -6 2 -5 3 4 a 4 b 5 c 4 b 5 Yes; no two ordered pairs have the same x-value. No; two ordered pairs have the same x-value. No; several ordered pairs have the same x-values. Yes; no two ordered pairs have the same x-value.

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Math 8H Heath 12.3 Exponential Functions Heath Algebra 1 McDougal Littell JoAnn Evans

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Exponential functions are functions in the form

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When a > 1, the graph will be a smooth curve that approaches the x-axis on the left and rises faster and faster as you move from left to right. When 0 < a < 1, the graph will be a smooth curve that falls faster and faster as you move from left to right and approaches the x- axis on the right. This graph shows exponential growth. This graph shows exponential decay.

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Graph an exponential function with a > 1. x-3-20123 f(x) Does this graph show exponential growth or decay? f(x) x

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x-3-20123 f(x) x-3-20123 f(x) Transformation of an Exponential Function This function shifted the graph of f(x)=2 x three units UP. Look at the table of values for the previous graph f(x) = 2 x. How will the table of values for the new function be different? Each y-value will be 3 greater than in the previous graph. f(x) x

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Transformation of an Exponential Function This function shifted the graph of f(x)=2 x two units DOWN. Look at the table of values for the original graph f(x) = 2 x. How will the table of values for the new function be different? x-3-20123 Each y-value will be 2 less than in the original graph. f(x) x

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5 units UP 3 units DOWN 1 unit UP

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Transformation of an Exponential Function This function shifted the graph of f(x)=2 x one unit to the left. What transformation do you think this graph will show? x-3-20123 f(x) x

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Graph an exponential function with a < 1. x-3-20123 Does this graph show exponential growth or decay? f(x) x

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Transformation of an Exponential Function x-3-20123 This function caused a shift of two units to the RIGHT. f(x) x

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One graph is a reflection of another graph in the x-axis if the two graphs are mirror images of each other. f(x) x

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Describe the relationship between the graph of function f and the graph of function g. Vertical shift; 4 units UP Vertical shift; 2 units DOWN Horizontal shift; 1 unit RIGHT Reflection Horizontal shift; 2 units LEFT Reflection

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Extra Practice: f(x) x-3-201 f(x)

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x01234 f(x)

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2.6 Families of Functions Sets of functions, called families, in what each function is a transformation of a special function called the parent. Linear.

2.6 Families of Functions Sets of functions, called families, in what each function is a transformation of a special function called the parent. Linear.

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