Name Math 125 Exam 3 Review. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Name Math 125 Exam 3 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. All of the values of functions g and f are shown in the given table. 1) Find (f g)(3) 1) x g(x) x f(x) Objective: (5.1) Find Value of Composite Function from Table Find the indicated composite for the pair of functions. 2) f(x) = x - 5 ; g(x) = 3x Find (g f)(x) x Objective: (5.1) Find and Evaluate Composite Function 2) Use the graph to evaluate the expression. 3) (f g)(-1) 3) 3 Objective: (5.1) Find Value of Composite Function from Graph Find the inverse of the given function. 4) f(x) = 7x ) f -1 (x) = 5x Objective: (5.2) Find Inverse Function Algebraically 1

2 Solve the problem. 5) Complete the table below by using the table of values for f to complete the table of values for f -1. 5) x f(x) x f -1 (x) x f(x) x f -1 (x) Objective: (5.2) Evaluate Function or Inverse Function Refer to the graph of the invertible function g to solve the problem. 6) Find g(8) 6) 4 Objective: (5.2) Analyze Graph of Invertible Function 2

3 Sketch the graph of the given function, its inverse, and y = x on the same set of axes. Graph the function with a solid line, and graph y = x and the function's inverse using dotted lines. 7) f(x) = 2x - 2 7) Objective: (5.2) Graph Inverse of a Function Find the logarithm. 8) log 5 (25) 8) 2 9) log(10) 9) 1 Find the inverse of the given function. 10) log 3 (x) 10) 3 x Objective: (5.3) Find Inverse Function 11) 5 x 11) log 5 (x) Objective: (5.3) Find Inverse Function 3

4 Sketch the graph of the function. 12) y = log 5 (x) 12) Objective: (5.3) Graph Logarithmic Function 4

5 13) y = log 1/3 (x) 13) Objective: (5.3) Graph Logarithmic Function Solve the problem. 14) The ph of a solution ranges from 0 to 14. An acid has a ph less than 7. Pure water is neutral and has a ph of 7. The ph of a solution is given by ph = - log(h + ) where H + represents the concentration of the hydrogen ions in the solution in moles per liter. Find the ph if the hydrogen ion concentration is 1 x Objective: (5.3) Solve Apps: Logarithms 14) Write the equation in exponential form. Assume that all constants are positive and not equal to ) log 4 = -2 15) = 1 16 Objective: (5.4) Convert Logarithmic Form to Exponential Form 16) log 9 (3) = ) 9 1/2 = 3 Objective: (5.4) Convert Logarithmic Form to Exponential Form 5

6 Evaluate. 17) Let f(x) = log 3 (x). Find f -1 (3) 17) 27 Objective: (5.3) Evaluate Function Find the logarithm. 18) log b ( b) 18) ) log 5 ( 1 25 ) 19) -2 Write the equation in logarithmic form. Assume that all constants are positive and not equal to 1. 20) 7 2 = 49 20) log 7 (49) = 2 Objective: (5.4) Convert Exponential Form to Logarithmic Form 21) e d = q 21) loge(q) = d Objective: (5.4) Convert Exponential Form to Logarithmic Form Solve. 22) log 6 (x + 3) = -1 22) Objective: (5.4) Solve Logarithmic Equation MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 23) log (x) = 4 23) A) 4000 B) 10,000 C) 40 D) 400 B Objective: (5.4) Solve Logarithmic Equation SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 24) log 9 (x 2 ) = 4 24) 81, -81 Objective: (5.4) Solve Logarithmic Equation 6

7 Solve the equation. Round the solution to four decimal places, if necessary. 25) 3 x - 3 = 40-9(3 x ) 25) Objective: (5.4) Solve Exponential Equation Use "intersect" on a graphing calculator to solve the equation. Round the solution to the fourth decimal place. 26) 2 x = 7 - x 26) Objective: (5.4) Solve Equation Graphically Solve. Round any approximate solution to the fourth decimal place. 27) 2 7x = ) Objective: (5.4) Solve Exponential Equation Solve the problem. 28) Bianca borrowed $12,000 at a rate of 6% compounded annually. What was the total amount Bianca owed after 8 years? $19, Objective: (5.5) Solve Apps: Compound Interest 28) 29) Solve ab cx+d + k = h for x. Assume that b > 0, b 1, and that the constants have values for which the equation has exactly one real number solution. x = log h - k a c log (b) - d log (b) Objective: (5.4) Know the Power Property for Logarithms 29) Find the logarithm. 30) log 3 ( 3) 30) 1 2 Solve the problem. 31) A storage tank contains radium, which has a half-life of 1600 years. i) Let f(t) represent the percent of the radium that remains in the tank at t years after the element was placed in the tank. Find an equation for f. ii) Predict when 20% of the radium will remain. 31) i) f(t) = 100( 1 2 )t/1600 or f(t) = 100( ) t ii) 3716 years Objective: (5.5) Solve Apps: Half-Life 7

8 32) A scientist wants to estimate the age of a piece of wood. The half-life of carbon-14 is 5730 years. Let f(t) represent the percent of carbon-14 that remains in the wood at t years after the wood dies. i) Find an equation for f. ii) If 20% of the carbon-14 remains, how old is the wood? 32) i) f(t) = 100( 1 2 )t/5730 or f(t) = 100( ) t ii) 13,300 years Objective: (5.5) Solve Apps: Half-Life Simplify. Write the expression as a single logarithm with a coefficient of 1. 33) 3 log b (t) - log b (s) 33) log b t3 s Objective: (5.6) Write Expression as Single Logarithm 34) 5 log b (2x 7 ) - 3 log b (4x 4 ) 34) x log 23 b 2 Objective: (5.6) Write Expression as Single Logarithm Solve. If necessary, round the answer to two decimal places. 35) log5 (9) - log5 (x) = 3 35) Objective: (5.6) Solve Logarithmic Equation Use a calculator to find the natural logarithm. Round your result to the fourth decimal place. 36) ln(80) 36) Objective: (5.7) Find Natural Logarithm Using Calculator Find the natural logarithm. 37) ln(e 9 ) 37) 9 Objective: (5.7) Find Natural Logarithm Evaluate. Round your result to the fourth decimal place. 38) log 20 (74.5) 38) Objective: (5.6) Use Change of Base Formula to Evaluate Logarithm 8

9 Solve the problem. 39) The function y = 800e x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 800 pounds of the material are initially put into the vault, how many pounds will be left after 170 years? 149 pounds Objective: (5.7) Solve Apps: Exponential Models with Base e 39) Solve the equation. Round the solution to four decimal places, if necessary. 40) e 5x - 1 e 5x = ) Objective: (5.7) Solve Equation Involving e or ln 9

Name Math 125 Exam 3 Review. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Name Math 125 Exam 3 Review. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Name Math 125 Exam 3 Review SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. All of the values of functions g and f are shown in the given table. 1) Find