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# Math 107 Quiz 3

IN ORDER TO GET FULL CREDIT FOR EACH PROBLEM, PLEASE SHOW ALL WORK AND WRITE EVERYTHING OUT CORRECTLY USING THE LANGUAGE OF MATH.The quiz is worth 100 points. Each problem is worth 5 points.1.For the given graph, please determine the intervals where the graph is(a) increasing, (b) decreasing, or (c) constant.2.Determine the intervals where the graph is increasing, and also any relative maxima or minima.3. (a) The area of a rectangle formula is A = lw. Suppose thatthe width is 5 less than the length. Expressarea as afunction of the width.(b) Use the function that you got from (a) to find the areawhen the width is 10 inches. Please make sure to givean appropriate unit of area.4. A hot-air balloon rises straight up from the ground at a rate of 120 ft/min.The balloon is tracked from a rangefinder on the ground at point P, which is400 ft from the release point Q of the balloon. Let d = the distance from theballoon to the rangefinder and t = the time, in minutes, since the balloon wasreleased. Express d as a function of t. (HINT: Please use the PythagoreanTheorem which says a2 + b2 = c2).5. Graph the piecewise function given byThen, determine the domain and range.6. Given the function f( x ) = x3 – x + 20 and g( x ) = 10×2, findeach of the following (NOTE: each part is independent fromthe other).(a) (f + g)(x)(b) (g – f)(x)(c) (ff)(x)(d) (gf)(x)(e) (f/g)(x)7. Given the function f( x ) = x3 – x + 20 and g( x ) = 10×2, findeach of the following (NOTE: each part is independent fromthe other).(a)(b)(c)8. Given the revenue function, R(x) = 60x – .4×2 and the cost function,C(x) = 3x + 13, and using the fact that P(x) = R(x) – C(x), please find(a) P(x)(b) P(10)9. Given that f( x ) = x2, please find the difference quotient, .10. The graph of y = f( x ) is the first graph shown and y = g( x ) is the graphshown just underneath that. (No formulas are given.) Please choose whichbest describes the relationship between the two graphs. HINT: Please findpoints on each of y = f( x ) and y = g( x ) and compare the points on y = f( x )and y = g( x ).(a) g( x ) = f( x + 1) – 2(b) g( x ) = f( x – 1 ) + 2(c) g( x ) = f( x + 2 ) + 1(d)g( x ) = f( x – 2 ) + 111. In the following sentence, please fill in each blank witheither of the words “up”, “down”, “right”, or “left”.The graph of y = | x + 7 | – 2 is the graph of y = | x | moved_______ 7 units and ______ 2 units.12. Given that (3, 4) and (1, -2) are points on the graph of y = f( x ), pleaselist each of the corresponding points on the graph of y = -f( x ).13. Given that (3, 4) and (1, -2) are points on the graph of y = f( x ), pleaselist each of the corresponding points on the graph of y = 4f( x ).14. Please feel free to use the graph of the equation or test algebraically todetermine the kinds of symmetry that each of the following equations have.(a) y = | 5x |(b) xy = 12(c) y = 1(d) x2 + y2 = 915. Please feel free to use the graph of the equation or test algebraically todetermine whether the following equation is an odd function, an evenfunction, a function that is neither odd nor even, or a function that is bothodd and even.(a) y = | 5x |(b) xy = 12(c) y = 1(d)16. Find a point that is symmetric to (1, 2) with respect to the x-axis,y-axis, and the origin.FOR #17 AND #18, FIND THE VARIATION CONSTANT AND ANEQUATION OF VARIATION FOR THE GIVEN SITUATION.17. y varies directly as x, and y = .1 when x = .2.18. y varies inversely as x, and y = .2 when x = 35.19. The weight M of an object on the moon varies directly as its weightE on earth. A person weighs 169.76 lbs on earth weighs 28.86 lbson the moon. How much would a 241.76-lb person weigh on themoon?20. The stopping distance d of a car after the brakes have been appliedvaries directly as the square of the speed r. If a car traveling60 mph can stop in 200 ft, how fast can a car travel and will stop in72 ft?