Math 111 Exam 1. Instructions

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1 Math 111 Exam 1 Instructions Please read all of these instructions thoroughly before beginning the exam. This exam has two parts. The first part must be done without the use of a calculator. When you are finished with Part I, turn it in. You will then receive Part II. You may use your calculator throughout Part II. Keep in mind, though, that you still must show your work. Answers alone will not receive credit. Once you have started Part II, you may not return to Part I. If you need to use the restroom during the exam, please place your phone on my desk before exiting the room. Throughout both parts of this exam, show all your work and write as neatly as possible. You may use scratch paper, but only what is written on your exam will be graded. Follow the same writing guidelines that are required for written assignments, including the following: Simplify all expressions as much as possible. Show your steps vertically. Use equal signs appropriately and align them. Always give an exact answer first. If rounding, make sure to show that your answer is approximate. Label and scale your axes when graphing. All application problems should be answered using a complete sentence and appropriate units. Additionally, you must define all variables you use in application problems. Take your time and check your answers. Breathe. There are 150 points possible.

2 Name: 150 Points Instructor: A.E.Cary 1. Let k(x) = (a) Find (g k)( 3). Math 111 Exam 1 Part I: No Calculator x + 7, g(x) = x 3 2x +, and f(x) = x2 + 2x 15. (b) Solve g(x) = 3. Clearly state the solution set. [6 points, 6 points] Instructor: A.E.Cary Math 111 Exam 1 Part I: No Calculator Page 1 of 7

3 k(x) =, g(x) = x 3 x + 7 2x +, f(x) = x2 + 2x 15 (c) Algebraically determine if f is even, odd, or neither. Show all justification and clearly state your answer. (d) Find and fully simplify f(x + h). (e) State the domain of the function k using set-builder notation and using interval notation. Show any supporting work below. Interval Notation: Set-Builder Notation: [6 points, 6 points, 8 points] Instructor: A.E.Cary Math 111 Exam 1 Part I: No Calculator Page 2 of 7

4 k(x) = (f) Find and fully simplify, g(x) = x 3 x + 7 2x +, f(x) = x2 + 2x 15 ( ) f (x). g (Bonus) State the domain of f g : 2. For each relation below, determine if y is a function of x. Clearly state and justify each response. (a) 2x + 3y = 12 (b) x y [6 points; 6 points, 6 points] Instructor: A.E.Cary Math 111 Exam 1 Part I: No Calculator Page 3 of 7

5 3. A fly is buzzing around in someone s garden. Its height h(t) (measured in feet) after t seconds is modeled in Figure 1. Use the graph of y = h(t) to answer the following. Approximate where necessary. (a) State the interval(s) over which h is decreasing. Figure 1. Graph of y = h(t) y 10 8 (b) State the interval(s) over which h is concave up. 6 2 (c) Find and interpret h(1) t (e) Solve and interpret h(t) = 3. (f) State any local minimum values and where each occurs. If none exist, state none. (g) State any absolute maximum values and where each occurs. If none exist, state none. [2 points ( points each)] Instructor: A.E.Cary Math 111 Exam 1 Part I: No Calculator Page of 7

6 . The piecewise-defined function w is graphed in Figure 2. Assume the parabola-looking piece is in fact a parabola. (a) State the domain of w using interval notation. (b) State the range of w using interval notation. (c) Write the definition (aka the formula) for w. Figure 2. Graph of y = w(x) y x The graph of y = 5(x 7) + 3 is a transformation of one of the basic (or original ) functions. Identify the basic (or original ) function and state each step to this transformation in an appropriate order. [ points, points, 16 points; 12 points] Instructor: A.E.Cary Math 111 Exam 1 Part I: No Calculator Page 5 of 7

7 . Let g(x) = 2 x This graph is a transformation of one of the basic or original functions. (a) Identify the basic or original function for this transformation and list all steps to this transformation in an appropriate order. (b) Use transformations to sketch the graph of y = g(x). Start with the graph of the original function and show all stages. Be sure to include at least three key points. Make sure that the final graph is clear. Figure 3. Graph of y = g(x) [8 points, 12 points] Instructor: A.E.Cary Exam 1 Part II: Calculator Required Page of 7

8 Name: Instructor: A.E.Cary Math 111 Exam 1 Part II: Calculator Permitted Let V (t) be the volume (in liters) of air in Batman s lungs after t seconds. This is modeled by: V (t) = 0.078t t t, 0 t 5 etermine the maximum amount of air in Batman s lungs and when this occurs. Round each value accurate to three decimal places.. The point (, 16) is on the graph of y = h(x). Determine the point on the graph of... (a) y = h(x 5) + 1 (b) y = 1 8 h( x) [8 points; 6 point, 6 points] OVER Instructor: A.E.Cary Exam 1 Part II: Calculator Required Page of 7

Math 19 Practice Exam 2B, Winter 2011

Math 19 Practice Exam 2B, Winter 2011 Name: SUID#: Complete the following problems. In order to receive full credit, please show all of your work and justify your answers. You do not need to simplify your