# lecture4 - sample of 80 mg ±nd an expression for m t the...

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Lecture 4: New Functions from old Exponential Functions(Sections 1.3, 1.5) ex. If f ( x ) = 1 x and g ( x ) = p x ± 1, ±nd with domain: 1) ( f + g )( x ) 2) ( fg )( x ) Function Composition Def. ( f ² g )( x ) Def. ( g ² f )( x )

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ex. If f ( x ) = 1 x and g ( x ) = p x ± 1, ±nd with domain: 1) ( f ² g )( x ) 2) ( g ² f )( x ) 3) If h ( x ) = x 2 , ±nd h ² g ² f and its domain.
Exponential Functions Def. An exponential function with base a is a function of the form f ( x ) = a x where a is a positive constant. NOTE: For exponential function f ( x ) = a x and positive integer n , 1. If x = n , then f ( x ) = 2. If x = 0, then f ( x ) = 3. If x = ± n , then f ( x ) = 4. If rational number x = p q for integers p and q , q > 0, then f ( x ) = 5. If x is irrational

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Graphs of Exponential Functions Graph on the same axes: 1) f ( x ) = 1 x 2) f ( x ) = a x , a > 1 3) f ( x ) = a x , 0 < a < 1 6 - ? ±
ex. Sketch the graph: y = 2 x +1 ± 3 6 - ? ± Laws of Exponents 1) a x + y = 2) a x ± y = 3) ( a x ) y = 4) ( ab ) x =

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Applications ex. The half-life of Strontium-90 is 25 yrs. In a

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Unformatted text preview: sample of 80 mg, ±nd an expression for m ( t ), the amount remaining after t years. ex. Suppose you invest \$1000 in an account that doubles every 6 years. What will the value of the account be in 24 years? Find a formula for the value in t years. The base e Consider the slope of the tangent line to the graph of f ( x ) = a x at the point (0 ; 1). If a = 2 6-? ± If a = 3 6-? ± Def. e is the number such that the slope of the tangent line to y = e x at x = 0 is exactly 1. NOTE: e ± ex. Sketch the graph of y = e x . 6-? ± Sketch the graph of the following: ex. y = e ± x 6-? ± ex. y = 2 ± e ± x 6-? ±...
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lecture4 - sample of 80 mg ±nd an expression for m t the...

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