Math 1050 Review KEY for Exam 1. Use synthetic division to find the quotient and the remainder. 1) x3 - x2 + 6 is divided by x + 2

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1 Math 0 Review KEY for Eam 1 Use snthetic division to find the quotient and the remainder. 1) is divided b + 2 Use snthetic division to determine whether - c is a factor of the given polnomial. 2) ; + 6 Find the real solutions of the equation. 3) = 0 4) 4( + 1)2 + 14( + 1) + 6 = 0 1

2 ) + = 20 6) 1 (- 2) = 3 7) = 0 8) 2/3-41/3 - = 0 2

3 Graph the equation b plotting points. 9) = List the intercepts for the graph of the equation. ) = ) = List the intercepts of the graph.tell whether the graph is smmetric with respect to the -ais, -ais, origin, or none of these. 12)

4 13) ) Draw a complete graph so that it has the given tpe of smmetr. 1) Smmetric with respect to the -ais (2, 0) (3, 1) 4

5 Determine whether the graph of the equation is smmetric with respect to the -ais, the -ais, and/or the origin. 16) = 0 17) = ) =

6 Write the standard form of the equation of the circle. 19) Write the standard form of the equation of the circle with radius r and center (h, k). 20) r = 3; (h, k) = (-6, 2) 21) r = ; (h, k) = (0, 6) 6

7 Find the center (h, k) and radius r of the circle with the given equation. 22) ( + 6)2 + ( + 8)2 = 49 23) ( + )2 + 2 = 16 24) 2( + 4)2 + 2( + 1)2 = 28 Find the center (h, k) and radius r of the circle. Graph the circle. 2) =

8 Find the general form of the equation of the the circle. 26) Center at the point (2, -3); containing the point (, -3) Determine whether the relation represents a function. If it is a function, state the domain and range. 27) Alice Brad Carl cat dog 28) {(-1, -3), (-2, -2), (-2, 0), (2, 2), (14, 4)} Determine whether the equation defines as a function of. 29) 2 = 8-2 8

9 30) = ± ) = Find the value for the function. 32) Find f(3) when f() = ) Find f(-2) when f() =

10 34) Find f(-) when f() = ) Find -f() when f() = ) Find f( + h) when f() = Find and simplif the difference quotient of f, 37) f() = 2 f( + h) - f(), h 0, for the function. h

11 Solve the problem. 38) If a rock falls from a height of 90 meters on Earth, the height H (in meters) after seconds is approimatel H() = When does the rock strike the ground? Round to the nearest hundredth, if necessar. Find the domain of the function. 2 39) g() = ) f() = 12-41) - 11

12 42) f() = ) f() = For the given functions f and g, find the requested function and state its domain. 44) f() = 7-2; g() = Find f + g. 4) f() = 9-9; g() = 4-7 Find f - g. 12

13 46) f() = ; g() = 22-1 Find f g. 47) f() = ; g() = 4-1 Find f g. Solve the problem. 48) Find (fg)(-) when f() = - 1 and g() =

14 Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if an, and an smmetr with respect to the -ais, the -ais, or the origin. 49) ) The graph of a function f is given. Use the graph to answer the question. 1) Use the graph of f given below to find f(16)

15 2) Is f(-) positive or negative? - - 3) Is f(3) positive or negative? - - 4) For what numbers is f() = 0?

16 ) For what numbers is f() > 0? - - 6) For what numbers is f() < 0? ) What is the domain of f?

17 8) What are the -intercepts? - - 9) What is the -intercept? ) How often does the line = -0 intersect the graph?

18 61) How often does the line = intersect the graph? ) For which of the following values of does f() = -16? A) -16 B) 12 C)8 D) 0 Answer the question about the given function. 63) Given the function f() = , is the point (2, -7) on the graph of f? 18

19 64) Given the function f() = 2-3, if = -1, what is f()? What point is on the graph of f? - 2 6) Given the function f() = 2 + 4, list the -intercept, if there is one, of the graph of f. + 9 The graph of a function is given. Decide whether it is even, odd, or neither. 66)

20 67) ) Determine algebraicall whether the function is even, odd, or neither. 69) f() = ) f() =

21 71) f() = 2 + The graph of a function f is given. Use the graph to answer the question. 72) (-8, ) (2.2, 3.9) (-, 0) (4, 0) - (-9., 0) (0, 0) (, -2.) (-2., -3.3) - Find the numbers, if an, at which f has a local minimum. What are the local maima? 21

22 Graph the functions. 73) f() =

23 74) f() = if < if ) f() = 1 if 0 < 3 if 3 < 7 if

24 Locate an intercepts of the function. 76) f() = if < if 1 The graph of a piecewise-defined function is given. Write a definition for the function. 77) (0, 4) (3, 2) (-3, 0)

25 Solve the problem. 78) Suppose that the -intercepts of the graph of = f() are 2 and 3. What are the -intercepts of = f( - 6)? Using transformations, sketch the graph of the requested function. 79) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing the function F(), where F() = f( + 2) - 1. (-1, 1) - (-3, -2) - (3, -4) 2

26 Complete the square and then use the shifting technique to graph the function. 80) f() = Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 81) f() =

27 82) f() = Find the function. 83) Find the function that is finall graphed after the following transformations are applied to the graph of =. The graph is shifted right 3 units, stretched b a factor of 3, shifted verticall down 2 units, and finall reflected across the -ais. Graph the function b starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. 84) f() =

28 8) f() = -2( + 1) Solve the problem. 86) Bob wants to fence in a rectangular garden in his ard. He has 70 feet of fencing to work with and wants to use it all. If the garden is to be feet wide, epress the area of the garden as a function of. 28

29 87) A wire 20 feet long is to be cut into two pieces. One piece will be shaped as a square and the other piece will be shaped as an equilateral triangle. Epress the total area A enclosed b the pieces of wire as a function of the length of a side of the equilateral triangle. What is the domain of A? 88) A bo with an open top is to be constructed from a rectangular piece of cardboard with dimensions 14 inches b 30 inches b cutting out equal squares of side at each corner and then folding up the sides as in the figure. Epress the volume V of the bo as a function of

30 89) The price p and the quantit sold of a certain product obe the demand equation: p = , { 0 800} 8 What is the revenue to the nearest dollar when 00 units are sold? 90) Let P = (, ) be a point on the graph of =. Epress the distance d from P to the point (1, 0) as a function of. A) d() = B) d() = C)d() = D) d() =

31 91) Two boats leave a dock at the same time. One boat is headed directl east at a constant speed of 3 knots (nautical miles per hour), and the other is headed directl south at a constant speed of 22 knots. Epress the distance d between the boats as a function of the time t. 31