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# Eponential, and Composite functions, Test three study guide MATH 1101

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This 3 page Study Guide was uploaded by Rukeem Collins on Tuesday March 22, 2016. The Study Guide belongs to MATH 1101 at Georgia State University taught by Changyong Zhong in Winter 2016. Since its upload, it has received 26 views. For similar materials see INTRO TO MATHEMATICAL MODELING in Geography at Georgia State University.

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Date Created: 03/22/16

Test 3 study guide One-to-one functions .One-to-one functions are functions where each output corresponds with one input. .Non-horizontal one to one functions are one to one. . Quadratic functions are not one to one. . You can test if a function is one to one on a graph by looking at the horizontal lines on the graph. If each line crosses the function only ounce, the function is one to one. Inverse of functions .The inverse of a function is the result of switching the domain and the range of a function. .To get the inverse of a function you switch the x and y values. . Only one-to-one functions have inverses. . A function is only inverse if Y=F(X) and X=G(Y) .Ex: X: 1, 4, 6 - X: 2, 7,9 Y: 2, 7, 9 Y: 1, 4, 6 Composite functions. .Composite functions are the result of combining multiple functions into one function. . (FG)(x) = F (G(x) . (FG)(x) Doesn’t usually equal (GF)(x) Ex: F= 3x+1 G= 2x-5 (FG)(x) = F (G(x) = 3(2x-5) +1= 6x-14 Getting the inverse of a function . To get the inverse of a function . Verify it’s one-to-one . Switch x and y . Solve Y . The graph of a function and its inverse will be mirrors of each other. Exponential functions . Exponential functions are Functions were the exponent is variable, and A is more than zero, and doesn’t equal 1. . The domain is all real numbers. . The range is everything above zero, but it can be changed if the function transforms. .There is no x, intercept, X is instead a horizontal asymptote. 0 . The y intercept is A (0, 1) . If A >1 the function is increasing. . If A< 0 the function is decreasing. Applications of exponential functions . Exponential functions can be used to find the value of an investment with compounding Interest. . The function for this is ???? = ????(1 + ) ???? t c ???? . P is the initial money put in, r is the interest rate (if negative it’s decreasing.) T is time, C is how often the interest rate compounds. . If the rate compounds quarterly, C= 4 if monthly, C=12 etc. . If the interest rate compounds continually, the equation is Pe . E is a constant. Logs Logs are Portions of tree trunks or limbs that have fallen that are often used for lumber (just kidding) . Logs are a form of exponential equations. . You get the log form of an equation by moving the base to immediately behind the log, setting your answer next, and setting your exponent to the answer of the log function. 2 . EX: 3 =9 turns into logɜ9=2 Transformations .Exponential functions can move based on their values. . In F(x)+k k is the vertical movement of the function. . In F(x+k) is k

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