Math 103 Intermediate Algebra Test 4 Review. c) 5 10x. 2. Evaluate the expression. Round your answer to three decimal places.

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1 Math 10 Intermediate Algebra Test Review Test covers Sections I. Epressions 1. Simplify the epression. a) b) 10e e 1 c) e 10 d) 16e e) e (e ). Evaluate the epression. Round your answer to three decimal places. a) 7e b) 7 c) 6 7e 1e d) 7 1e. Evaluate the logarithm without using a calculator. If not possible, state why. a) log 16 c) 1 1 log 8 e) log 16 b) log d) log 9 f) log Assume log a , log a , and log Find the following. a. 1 a) log a 1 b) log a c) log a d) 9 log a. Use a calculator to evaluate the logarithm by means of the change-of-base formula. Round to four decimal places. a) log 7 b) log 1 9 c) log 1 1 Math Resource Center Saginaw Valley State University

2 Math 10 Test Review p 6. Use properties of logarithms to condense the epression. a) log log 6 c) e) log log log 7ln n b) log 7 y log 7 d) log( ) f) 1 log ( ) log 7. Use properties of logarithms to epand the epression. a) log 17 c) ln y z e) ln ( ) b) log 9 d) log 10 ( ) f) log yz II. Equations 1. Write in eponential form. a) log 81 b) log 1 c) log. Write in logarithmic form. a) = 1 b) c) = b y. Solve. Round your answer to three decimal places a) 6 c) 1 b) e 1 d) 6 =

3 Math 10 Test Review p. Solve. a) log log c) ln( + ) ln( ) = 0 b) log + log( ) = 1 d) log ( 6) log IV. Functions 1. Write the equation of the parabola in standard form and find the verte of its graph. a) y = + 8 b) y = 6 c) y = Sketch the parabola. Identify any verte and any -intercepts. a) y = + c) y = ( + ) b) y = d) y = 1 ( 6 8)

4 Math 10 Test Review p. Find the and y-intercepts (if any) of the graph of the following functions. a) y = + + c) y = + 9 b) y = + d) y = Evaluate the function as indicated. If necessary, round your answer to three decimal places. a) f() = , at = 10 b) h() =, at = 0.7e. Sketch the graph of the function. Label the horizontal asymptote and some specific points. a) f() = e c) g() = e b) h() = e d) f() = e +

5 Math 10 Test Review p 6. Let f() = and g() = +. Find: a) (f g)() b) (g f)( ) c) (g f)( ) d) (f g)() 7. In each part, given f() and g(), find (i) (f g)(), (ii) (g (iv) (g g)(). a) f() = 1, g() = + 7 i) ii) f)(), (iii) (f f)(), and iii) iv) b) f() = +, g() = + i) ii) iii) iv) c) f() = +, g() = +

6 Math 10 Test Review p 6 i) ii) iii) iv) 8. Use the horizontal line test to determine if the function is one-to-one. a) y = f() b) y = h() 9. Verify algebraically that the two functions are inverses of each other. 1 a) f() = +, f ( ) b) g() =, g 1 () = Find the inverse of the function. Graph the function and its inverse on the same set of

7 Math 10 Test Review p 7 aes. a) f() = + c) f() = 1, > 0 b) g ) 1 6 ( 11. Sketch the graph of the function. Label the vertical asymptote and some specific points. For each graph, state the equation of the vertical asymptote. a) f() = log c) h() = log

8 Math 10 Test Review p 8 vertical asymptote: vertical asymptote: b) g() = log + e) h() = log 1 vertical asymptote: vertical asymptote: V. Applications 1. A farmer wants to fence in three sides of a rectangular field with 1000 feet of fencing. The fourth side of the field will be along a river. Find the dimensions of the field that will make the enclosed area a maimum.. Working together, two people can complete a task in hours. Working alone, one person takes. hours longer than the other. How long would it take each person working alone?

9 Math 10 Test Review p 9. If an object is projected vertically upward from ground level with an initial velocity of 0 ft/sec, then its distance s above the ground after t seconds is given by s 16t 0t. For what values of t will the object be more than 16 feet above the ground? 1 1. The height y (in feet) of a ball that you throw is modeled by y, 0 10 where is the horizontal distance (in feet) from where you release the ball. a) How high is the ball when you release it? b) What is the maimum height of the ball? c) How far away is the ball from its original position when it lands?. A manager of an auto dealership bought several used cars of the same model for 1,000. When all but three of the cars had been sold at a profit of $000 per car, the original investment of $1,000 had been regained. How many cars were sold and what was the selling price of each?

10 Math 10 Test Review p You have $00 that you want to invest for years. You can either invest in a C.D. that pays.% interest compounded quarterly or a bank account that pays.% compounded continuously. Which is the better investment? The compound interest formula are: compounding n times a year for t years: continuous compounding: A P 1 rt A Pe r n nt 7. Sue s favorite department store is having a sale. As a loyal customer, she has also been sent a $ off coupon in the mail. a) Suppose p is the price of an item that Sue wants to buy. Write a function C in terms of p giving the price of the item after the coupon is used. b) The item that Sue wants to buy is 0% off. Write a function S in terms of p giving the price of the item after the 0% discount has been taken. c) Form the composite functions C S ( p) and S C ( p) and interpret each.