Math 103 Exam 3 Sample Exam. Name: Section: Date:

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1 Math 0 Eam Sample Eam Name: Section: Date: Signature: Do not start this test until your instructor says so. You will have eactly 0 minutes from this time to finish the test. Please show all work in the space provided. There are questions on pages. Without fully opening the eam, please check to make sure your eam is complete before you begin. Please read instructions carefully.. You will need a pencil or pen, one calculator and this eam paper. Please clear everything else from your desk. (Please turn off or switch cell phones to manner mode and place in backpack NOT on your person.). Calculators such as the TI89, TI-NSPIRE, Voyage 00, TI9, TI9+, HP9G, HP9G+, HP0G, Casio algef.0, algef.0pls or laptop, handheld, desktop and palmtop computers are NOT to be used. The use of cell phones, PDAs, Blackberries, head sets, or any other wireless device in the classroom is specifically prohibited. Please do not ask your instructor/proctors about calculator use or mode. You must clear all programs from your calculator memory. Calculators cannot be shared.. Please look at overhead/board for possible corrections to this eam.. Do not spend too much time on a particular problem. Work the problems that are simplest for you first.. There is no partial credit on the multiple choice or true/false questions. On the open-ended questions, the grading will be based on your method. SHOW ALL OF YOUR WORK. NO WORK NO CREDIT! DO NOT SKIP STEPS! You must show all work that supports your answer in order to get credit. Be neat and orderly. If you need additional space, use the back of the eam pages.. Circle the letter of the correct answer for multiple choice or true/false questions. For open-ended questions, place your work and answers in the space provided. Answers can be in any form unless otherwise specified. For problems asking for EXACT answers, leave in terms of fractions, π and number. No credit will be given for decimal approimations when an EXACT answer is required. When solving equations, please put your answer in solution set form. For decimal answers, round to decimal places unless otherwise specified. 7. Give measurement units (feet, degrees, etc.) when appropriate. 8. SIMPLIFY ALL ANSWERS as much as possible. Please Note: This is a practice eam. The actual eam may differ significantly from this practice eam because there are many varieties of problems that can test each concept.

2 Math 0 Eam Sample Eam. (0 points) Given the function f ( ) ( + 8) +, find (a) the coordinates of the verte (a) (b) the equation for the ais of symmetry (b) (c) the -intercept(s) (c) (d) the y-intercept(s) (d) (e) the domain and range of f (e) Domain: Range: 0. (8 points) Given, f ( ) +, +, if if if < <. (a) Evaluate f ( ) f ( ) f () +. f (0) (b) Evaluate ( f () ) f. 8

3 Math 0 Eam Sample Eam. (0 points) A rancher needs to build four identical pens for his animals as shown in the diagram below. He has 0 feet of fencing. He does not need to put the fence along the barn. Find the length and width that would maimize the area of the pens. What is the maimum area for each pen? BARN Length: Width: Maimum Area: 0. (0 points) Graph g ( ) f ( + ) where f ( ). To receive full credit, you must show your intermediate steps (tables or graphs). 7 y

4 Math 0 Eam Sample Eam. ( points) Use the graph of g ( ) to graph ) ( + ) Use dashed lines to indicate the asymptotes on your graph. f ( +. (a) Write the equation of the vertical asymptote(s), if any, of f. 7 y (b) Write the equation of the horizontal asymptote(s), if any, of f (c) Refer to your graph to complete each of the following statements. As, f ( ). As, f ( ). 8. (0 points) For f ( ) and g ( ) +, find (a) ( f + g)( ) and its domain. ( f + g)( ) Domain: f g (b) the domain of (). (c) ( f o g)( ) and its domain. ( g)( ) (d) ( f ( )) g. f o Domain: 0

5 Math 0 Eam Sample Eam 7. (0 points) For ( ) + f, find the inverse function f ( ). f ( ) 0 8. ( points) Refer to the graph at the right. (a) Find ( f g)(). (b) Find the domain of ( f + g) (). (c) Find ( f ( )) y y g() y f () g. Note: All endpoints are closed. (d) Find g (). (e) Is f even, odd, or neither? (f) Where is f decreasing? (g) Where is f ( ) < 0?

6 Math 0 Eam Sample Eam SHORT ANSWER: ( points each) 9. A polynomial of degree can have a maimum of turning points. 0. The graph of f ( ) + left and right.. Does f ( ) +, describe a polynomial function?. The degree of the polynomial function p ( ) ( ) ( + ) is.. If the point (, -) in on the graph of f, then the point is on the graph of f.. Is + y 9 a one-to-one function?. The equation for the horizontal asymptote ( ) 8 f is.. If g( ) g( ), then the graph of g reflects over the ais. Problem # Total Points Earned Possible