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Exponential Functions and Their Graphs
Sec. 5.1 Exponential Functions and Their Graphs
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Algebraic Functions Polynomial functions and rational functions
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Transcendental functions
Exponential functions and logarithmic functions
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Definition of Exponential Function
f(x) = ax a > 0, a ≠ 1, and x is a real number a is the base x is the exponent
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Natural Base Represented by e e ≈ 2.71828… (Irrational)
f(x) = ex is called the Natural Exponential Function
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Ex. 1 2-3.1 2-π
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Ex. 2 Evaluate and round to nearest thousandth
3.92.1 2-3π 4√5291
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Ex. 5 a) e-2 b) e-1 c) e1 d) e2
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Graph of Exponential Functions
f(x) = 2x g(x) = 4x x 2x 4x -2 -1 1 2 3
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F(x) = 2-x G(x) = 4-x x 2-x 4-x -3 -2 -1 1 2
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Note: the negative exponent reflects about the y-axis
Find for each Domain Range Intercept Direction Horizontal Asymptote Continuous?
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Graph on the calculator
h(x) = (½)x It is the same as f(x) = 2-x
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What will happen to the graph of f(x) = 2x
Which means 2x+2 f(x-3) f(x) + 3 Which means 2x + 3 f(x) – 2 -f(x)
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Summary Given f(x) = ax f(-x) = a-x f(x+b) = ax+b f(x-b) = ax-b
Reflects about y axis Horizontal left b units Horz. Right b units Vertical up b units Vertical down b units Reflects over x axis
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