0\u\S. Name: UC Davis MAT 012, Summer Session II, Midterm Examination. Student ID: DATE: August 21, TIME ALLOWED: 100 minutes INSTRUCTIONS

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1 UC Davis MAT 012, Summer Session II, 2018 Midterm Examination Name: 0\u\S Student ID: DATE: August 21, 2018 TIME ALLOWED: 100 minutes INSTRUCTIONS 1. TIns examination paper contains SEVEN (7) questions and comprises ELEVEN (11) printed pages. 2. This is a closed-book exam. 3. You may use a calculator, but to receive credit you must show all work. 1

2 UC Davis, Summer Sessioii II, 2018 Midterm Exam MAT 012 Exercise 1 Solve the following equations md inequalities t<3 4 i-2 -LI : (I 2. x2+x_6=o 4t42 C3) 3. x3+2x2 3x=O 2

3 (frt) Exercise 2 UC Davis, Summer Session II, 2018 Midterm Exam MAT 012 cq) 03 t b) What is the function that represents g(x) reflected across the x axis? Plot this function. I izr? x V I - a) What is the function that represents fix) reflected across the y &xis? Plot this function. 3. Consider the following transformations: Dciv... our c r cd cecd i1..-v1 (-5 2. Suppose f(x) = / x + 1 and g(x) = 3x 2. What is the domain of the composition fog? 0 Ai ccc KvvAsccR +t4 6) x A+ e CC) c(-t) 4e- a11 1. Describe the domain of the composition f a g(x) in terms of the domains off and g. Consider two functions f(x) and g(x).

4 ]C Davis! Summer Session II, 2018 Midterm Exam MAT 012 Exercise 3 Suppose (1, 1. What is (cd iv = L 3) - pclpe7uhieuhzr to 2- r&j I - C - I 1 3) and ( 1 1) are two points on the outside of a circle. the distance between these two points? 2. What is the midpoint of these two points? 3 k 7 UZ the line that connects the two points? 3. What is the equation for t(-(- 4. What is the equation for the line that passes through the mid point, arid is the line that connects the points? (\flc icvntti\ c

5 (3 \ NZ_ c-\ ) for all the points on the circle? (0 I ) 5. Suppose the midpoint of the two points is also the center of the circle. \Vhat is the equation S above, but whose center is the origin? 6. What is the equation for all the points on a circle that has the same radius as the circle UC Davis, Sinurner Session II, 2018 Midterm Exam MAT 012

6 UC Davis, Summer Session 11, 2018 Midterm Exam MAT 012 (a) Draw a picture that represents the situation. (h) Find the height of the top of the ladder as a function of the distance along the floor between the wall and the base of the ladder. (c) Find t he area of the triangle enclosed in the ladder, the wall and the floor, as a function of the distance along the floor between the wall and the base of the ladder. (3) C) [3) 6 Exercise 4 Suppose you are leaning a 3-meter ladder against a wall. 4 \2 k (e) What is the average rate of change of the area of the triangle enclosed by the ladder between when the floor distance is 0 meters and when it is 1 meter?

7 Consider the triangle below Exercise 5 h. (Recall that the area of a triangle is base height) -J 7 (c) What is the maximum area of the triangle? Th y c M tlh (i, cc 6%. IC> u1sc2-) TY < 9(&c Vc\c \ as c V : 2 -H) L;] Ccvptc1e i - t 2- (b) What length b maximizes the area of the triangle? (a) Write an equation that describes the area enclosed by the triangle as a function of the base Suppose that the height h and the base b add to 4. b UC Davis, Summer Session II, 2018 Midterm Exam MAT 012

8 UC Davis, Siinuner Session II Midterm Exam MAT 012 Exercise 6 ± 1). and h(s) = (s 1)( C4) t jfl N CkN A -4. One of the three flihctions f. g. and h has an inverse function. Which function is it, and why? Explain your answer either graphically or algebraically. 8 1)1. + 1)(x 2), g(x) = i)2(x 1. Graph f(s). Label all x-intercepts. Suppose f(x) = (x 2. Graph g(x). Label all x-intercepts. 3. Graph It(s). x in te ree pt S. (y ts caq L e c(lsc ii eftsct \4 test.

9 0 5. For the function you identified in the previous part, find its inverse function. 9 UC Davis, Summer Session II, 2018 Midterm Exam MAT 012

10 Exercise 7 and cc- us ni 0 ttvt C N-C\ C) 1 vvwcac C -v ( t )()kd% oo iodo. as,-)-ad, rj e?tc\u1 c frzw cioal C¼5 c-fl& J t:-q _7( J 10 TiC Davis. Sunmier Session II. 2018?Iitlterin Exam MAT Compare and contrast f and g using the following table. Identify at least 3 similarities and at least 3 (litferences. (Options include but are not limited to: domain, range, syninwtry, asymptotes, turning points, tnaxinta/nlinima, existence of an inverse Similarities Differences c-ny 9 n M -> 0. retk ttt%%s ç CP9vV ( a1z C & c-i- LiM t -a # c.s 3C3 t c i1 vi )3i nud C-ma-,. E J*; C)3k\ Cs c.%c SL,.y\ \,cak5ccs /v5cc rj(s) bil/ v\c\x;w( CC 1s. ) hcc oy\ dcts net. J c k *\-o C\V\ S çnc) dcc rcct2.cs Cfl o), (-c, b). 2. Graph f(x) translated to the left by 2 units. What equation describes tins function? A g(x) = 1flRW\ r c\ cfla MoC.5 q\cci. (ij.fla<ttit c&t Suppose f(x) = -

11 UC Davis, Stininier Session II, 2018 Hdterni Exam MAT Graph q(r) translated up iw 3 units. \Vliat equation describes this function? L) x 4. Plot the function y = Label all asymptotes. TY. 4 L $ i 14g -zi $ _ St i c_i. 5. Plot the hi ion y = 2 + Label all asymptotes. / L) I 11