MA 109 College Algebra EXAM 3 - REVIEW

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1 MA 9 College Algebra EXAM - REVIEW Name: Sec.:. In the picture below, the graph of = f(x) is the solid graph, and the graph of = g(x) is the dashed graph. Find a formula for g(x) x (a) g(x) =f(x) (b) g(x) =f(x) (c) g(x) =f ( x) (d) g(x) = f(x) (e) g(x) = f(x) Suppose that the graph of = f(x) contains the point (,). Find a point on the graph of = f(x).. Let f(x) = x +. Find the average rate of change of f(x) between x = and x =9. (a) 9/7 (b) 9 (c) 7/9 (d) 9/7 (e) 9. Suppose that the graph of = f(x) contains the point (,-). Find a point on the graph of = f(x)+7.

2 . Let f(x) =x +x. Find the average rate of change of f(x) from x = a to x = a + h. Assume h. (a) a h (b) ah + h +a +h h (c) (d) a + h + (e) h +h h. The mass m(t) remaining after t ears from a -gram sample of a radioactive elmement is given b m(t) =e.t. When will the mass remaining equal grams? Round our answer to the nearest hundredth of a ear. (a) About. ears (b) About. ears (c) About. ears (d) About. ears (e) About. ears 7. Solve. log (x ) + log (x +)= (a) x =and x = (b) x =and x = (c) x = (d) x = (e) x =and x =. Find all real solutions or state that there are NONE. e x =.

3 9. In the picture below, the graph of = f(x) is the solid graph, and the graph of = g(x) is the dashed graph. Find a formula for g(x) in terms of f(x) x. Suppose that the graph of = f(x) contains the point (-,7). Find a point on the graph of = f(x +).. Let f(x) =x +. Find the average rate of change of f(x) from x = to x =9. (a) (b) (c) (d) (e). Let f(x) =ln(x +7). Find f (x).. Let f(x) =e x+. Find f (x).

4 . The number of bacteria in a culture is modeled b the function n(t) =e.t where t is measured in hours. After how man hours will the number of bacteria reach 7? (a) About 9.9 hours (b) About.7 hours (c) About 7. hours (d) About. hours (e) About. hours. In the picture below, the graph of = f(x) is the solid graph, and the graph of = g(x) is the dashed graph. Use the graphs to evaluate f(g()) x Let f(x) = x and g(x) = x. Find the domain of (f + g)(x). 7. Let f(x) =x 7. Find f(f(x))

5 . If $ is invested at an interest rate of % per ear compounded quarterl, find the amount of the investment at the end of ears. (a) $. (b) $. (c) $.7 (d) $7. (e) $ You wish to purchase a new cell phone. You have a coupon for $ and the store is running a special which allows ou to deduct % from the price. If the original price of the cell phone is 7 dollars, what is the final price if ou appl the coupon and then appl the % discount.. Let h(x) =(x +). Find functions f(x) and g(x) such that h(x) =f(g(x)). (a) f(x) =(x +) and g(x) =(x +) (b) f(x) =x and g(x) =x + (c) f(x) =x +and g(x) =x (d) f(x) =xand g(x) =x + (e) f(x) =x +and g(x) =x. Which of the following functions are one-to-one? (a). a(x) = x (b). b(x) =x (c). c(x) =x + (d). d(x) = (e). e(x) =x (f). f(x) =x + (g). g(x) =(x +) (h). h(x) = x + (i). i(x) =x + (j). j(x) = x (k). k(x) = x (l). l(x) =

6 . Let f(x) = x and g(x) =x. Find the domain of. Let f(x) = x and g(x) =x. Find the domain of. Let f(x) = x + x. Find f (x). ( ) g (x). f ( ) f (x). g. Let f(x) =x +7x. Find f(x + h) f(x). h (a) x h 7 (b) h +7h h (c) h +7h (d) x +h +7 (e) xh +h +x +7h h ( ) x. log = z (a) log(x)/( log() log(z)) (b) log(x) log() + log(z) (c) log(x) + log() log(z) (d) log(x) log() log(z) (e) log(x)/log() log(z) 7. Let f(x) = log (x +7). Find f (x).

7 . The graph of the one-to-one function f is shown below. Find the domain of f x 9. Joni invests $ at an interest rate of % per ear compounded continuousl. How much time will it take for the value of the investment to quadruple? Round our answer to the nearest tenth of a ear. (a) 7. ears (b) 7. ears (c). ears (d).7 ears (e). ears 7

8 . The graph of the one-to-one function f is shown below. Find the range of f x. The graph of an exponential function, f(x) =a x is shown below. Find a. 9 7 (a) (b) (c) (d) (e) x

9 . Solve. log (x ) + log (x +)= (a) x = (b) x =and x = (c) x = (d) x =and x = (e) x =and x =. In the picture below, the graph of = f(x) is the solid graph, and the graph of = g(x) is the dashed graph. Use the graphs to evaluate g(f()). (a) (b) (c) (d) (e) x Let f(x) = log ( x). Find the domain of f(x). (a) (, ] (b) (, ) (c) [, ) (d) (, ) (e) (, ) 9

10 . Find the domain and range of =ln(x 7). (a) Domain: (, ) Range: [7, ) (b) Domain: (, ) Range: (7, ) (c) Domain: (, ) Range: (, ) (d) Domain: [7, ) Range: (, ) (e) Domain: (7, ) Range: (, ). ( ) x z log = (a) log (x)+ log (z) log () ( ) ( log (x)) log (z) (b) log () (c) x + z (d) log () log (x) log (z) ( ) (x) z (e) 7. Solve for x. log(x +)= (a) x = log() (b) x = (c) x = (d) x = (e) x = log()

11 . Let f(x) =x +. Find f (). (a) (b) (c) (d) (e) 9. Let f(x) =x and g(x) =x. Find g(f(x)). (a) x x + (b) x (c) x (d) x x (e) x +. Let f(x) =x +. Find the average rate of change of f(x) from x = to x =9. (a) (b) (c) (d) (e)

12 . Which of the following functions are one-to-one? f(x) =x + g(x) =x h(x) =x 9 (a) Onl f(x) and g(x) are one-to-one. (b) Onl g(x) and h(x) are one-to-one. (c) Onl h(x) is one-to-one. (d) None of the functions are one-to-one. (e) All of the functions are one-to-one.. Use a calculator to approximate log (). Your answer should be correct to decimal places. (a). (b).79 (c).97 (d). (e).7. Let f(x) =x +x +. Find f(x + h) f(x) h

13 . Let f(x) = ( ) f x +and g(x) =x. Find the domain of (x). g (a) (, ] (b) (, ) (, ] (c) [, ) (d) [, ) (e) [, ) (, ). You are going to purchase some memor for our computer. The original price of the memor is x dollars You have two coupons. The first coupon allows ou to take % off of the price. The second coupon allows ou to deduct $ from the price. Suppose that ou use the first coupon to take % off and then ou use the second coupon to deduct $ from the price. Find a formula for the final price P in terms of x. (a) P (x) =.x (b) P (x) =.x (c) P (x) =.x (d) P (x) =.x (e) P (x) =.x. Find the inverse function of f(x) =x.

14 7. Explain how the graph of g(x) =(x +) 9 is obtained from the graph of f(x) =x. (a) Shift left 9 units and shift down units. (b) Shift right units and shift up 9 units. (c) Shift right units and shift down 9 units. (d) Shift right 9 units and shift up units. (e) Shift left units and shift down 9 units.. Express the equation in logarithmic form. = (a) log = (b) log = (c) log = (d) log = (e) log = 9. Which of the following statements are true? (I) log () = (II) log( a )=log(a) log(b) for all positive a and b. b (III) ln(a + b) =(ln(a))(ln(b)) for all positive a and b. (a) Onl (I) and (II) are true. (b) Onl (III) is true. (c) Onl (I) and (III) are true. (d) Onl (I) is true. (e) Statements (I), (II), and (III) are all true.

15 . In the picture below, the graph of = f(x) is the solid graph, and the graph of = g(x) is the dashed graph. Find a formula for g(x). (a) g(x) =f ( x) (b) g(x) =f(x) (c) g(x) = f(x) (d) g(x) = f(x) (e) g(x) =f(x) x. Let f(x) = log ( x). Find the domain of f(x). (a) (, ) (b) [, ) (c) (, ) (d) (, ] (e) (, ). Use a calculator to approximate log (). Your answer should be correct to decimal places. (a).9 (b). (c).97 (d) -. (e).979