MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. C) ±

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1 Final Review for Pre Calculus 009 Semester Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation algebraically. ) v + 5 = 7 - v ) A) ± B) ± C) ± 5 D) ± 5 7 Find the domain of the given function. ) f(x) = 6 - x ) A) All real numbers B) ( 6, ) C) (-, 6] D) (-,6) (6, ) ) f(x) = x + (x + )(x - 5) A) All real numbers B) (0, ) C) (-, -) (- -) (-, 5) (5, ) D) [-, -) (-, 5) (5, ) ) x ) f(x) = x + x A) (-, 0) (0, ) B) (-, 0) (0, ) (, ) C) (-, -) (-, ) D) (-, -) (-, 0) (0, ) ) Find the range of the function. 5) f(x) = (x + ) + 6 5) A) [6, ) B) (6, ) C) (-, ) D) (-6, ) 6) f(x) = 5 - x 6) A) (0, ) B) (-, 5) (5, ) C) (-, 0) (0, ) D) (-, ) Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable.

2 7) g(x) = x + x x 7) A) No B) No

3 C) No D) Yes; removable 8) h(x) = x x - 8)

4 A) B) Yes; non-removable C) Yes; non-removable D) No No Solve the problem. 9) Use the graph of f to estimate the local maximum and local minimum. 9) A) Local maximum: approx. 8.08; local minima: approx and.75 B) Local maximum: ; local minima: - and C) No local maximum; local minimum: approx D) Local maximum: ; local minima: - and

5 Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. 0) y = 5-x + 0) A) Bounded above B) Bounded below C) Bounded D) Unbounded Determine algebraically whether the function is even, odd, or neither even nor odd. ) f(x) = 7x + 7x + 5 ) A) Even B) Neither C) Odd ) f(x) = x + x ) A) Neither B) Odd C) Even Find the asymptote(s) of the given function. ) f(x) = x - 5 vertical asymptotes(s) ) x - 9 ) g(x) = A) x = 5 B) x =, x = - C) x = - D) x = x - 5 vertical asymptotes(s) ) (x - 9)(x + 5) A) x = -9, x = 5 B) x = -5 C) x = 9, x = -5 D) x = 5 5) g(x) = x + 7 horizontal asymptotes(s) 5) x - A) None B) y = C) y = 0 D) y = -7 Match the function with the graph. 6) 6) A) y = x - B) y = x - C) y = x + D) y = x - - 5

6 7) 7) A) y = sin x + B) y = sin x - C) y = cos x + D) y = cos (x - ) 8) 8) A) y = ln x + B) y = -ln (x + ) C) y = -ln(x) D) y = -ln (x- ) Graph the piecewise-defined function. 9) 7x + 6, if x < 0 y(x) = x -, if x 0 9) 6

7 A) B) C) D) Perform the requested operation or operations. Find the domain of each. 0) f(x) = 5x + 5, g(x) = 6x - Find fg. 0) A) (5x + 5)(x - ); domain: (-, ) B) (5x + 5)(6x - ); domain: (-, ) C) (x - )( 5x + 5); domain: -, ) D) ( 5x + 5)( 6x - ); domain:, ) f(x) = 5x + 6, g(x) = 5x Find (f + g)(x). ) A) 5x + 0x; domain: (-, ) B) 5x + 6-5x; domain: (-, ) C) 5x x; domain: (-, ) D) 5x + 6 ; domain: (-, ) 5x Perform the requested operation or operations. ) f(x) = x + ; g(x) = 8x - 6 Find f(g(x)). A) f(g(x)) = x - B) f(g(x)) = 8 x - C) f(g(x)) = 8 x D) f(g(x)) = x + ) 7

8 ) f(x) = f(x) = x - 9 ; g(x) = x ) Find g(f(x)). A) g(f(x)) = (x - 9) x B) g(f(x)) = x x - 9 C) g(f(x)) = x - 9 D) g(f(x)) = x - 9 Find functions f and g so that h(x) = f(g(x)). ) y = x + ) A) f(x) = /x, g(x) = /x + B) f(x) = /x, g(x) = C) f(x) = x, g(x) = /x + D) f(x) = x +, g(x) = /x 5) y = x + 5) A) f(x) = x +, g(x) = B) f(x) = /x, g(x) = x + C) f(x) = / x, g(x) = x + D) f(x) =, g(x) = + Find two functions defined implicitly by the given relation. 6) x + y = 6 6) A) y = 6 + x or y = x B) y = 6 - x or y = 6 + x C) y = 6 - x or y = x D) y = 6 + x or y = 6 - x Find the (x,y) pair for the value of the parameter. 7) x = t and y = t - for t = 7) A) (6, ) B) (, 6) C) (, 6) D) (, ) 8) x = t - 5 and y = t for t = 8) A) 9, 6 B), 6 C) 6, - D) -, 6 Find a direct relationship between x and y. 9) x = 9t and y = t + 8 9) A) y = 6x + 8 B) y = 9 x + 8 C) y = x 9 D) y = 6x 0) x = t - 7 and y = t + 6t 0) A) y = x + 5x + 56 B) y = x + x + C) y = x - 8x + 7 D) y = x + 0x + 9 ) x = t and y = 7t - ) A) y = 6x - B) y = 7 x - C) y = 7 9 x - D) y = 7 x - 8

9 Find the inverse of the function. ) f(x) = x + 7 ) A) Not a one-to-one function B) f-(x) = x + 7 C) f-(x) = x - 7 D) f-(x) = x - 7 ) f(x) = -x - 7 9x - A) f-(x) = -x - 7 9x - B) f-(x) = 9x + x - 7 C) Not a one-to-one function D) f(x) = x - 7 9x + ) Determine if the function is one-to-one. ) ) A) No B) Yes 5) 5) A) No B) Yes 9

10 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. 6) f(x) = x + and g(x) = 9x - 6) 9 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 7) Let f(x) compute the cost of a rental car after x days of use at $9 per day. What is the interpretation of the solution of f-(x) = 86? A) The cost of rental for 9 days B) The cost of rental for 86 days C) The number of days rented for $9 D) The number of days rented for $86 7) Convert the angle to decimal degrees and round to the nearest hundredth of a degree. 8) 87 8) A) B) 87.0 C) D) 87.0 Convert the angle to degrees, minutes, and seconds. 9).7 9) A) 5 B) 6 C) 5 7 D) 7 Convert from degrees to radians. Use the value of found on a calculator and round answers to four decimal places, as needed. 0) 0 0) A) 7 B) 7 C) 7 D) Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. ) 55 ) 8 A) 75 B) 00 C) 9.59 D) 550 Use the arc length formula and the given information to find the indicated quantity. ) r = 5 ft, = ; find s ) A) 8 ft B) 0 ft C) ft D) 0 ft 6 Solve the problem. ) The radius of a car wheel is inches. How many revolutions per minute is the wheel making when the car is travelling at 5 mph. Round your answer to the nearest revolution. A) 9 rpm B) 56 rpm C) 66 rpm D) 5 rpm ) A car wheel has a 6-inch radius. Through what angle (to the nearest tenth of a degree) does the wheel turn when the car rolls forward ft? A).9 B).9 C) 8.9 D) 8.9 ) ) 0

11 Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. 5) 5) 0 6 Find sin A and cos A. A) sin A = 5 ; cos A = 5 B) sin A = ; cos A = C) sin A = 5 ; cos A = 5 D) sin A = 5 ; cos A = 5 Assume that is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. 6) sin = 7 ; cot 6) 8 A) 8 5 B) 7 5 C) 5 7 D) 5 8 Give the exact value. 7) cot 7) A) B) C) D) Solve the equation. 8) Solve sin = for, where ) A) 5 B) 90 C) 0 D) 60 Solve the problem. 9) A kite is currently flying at an altitude of 6 meters above the ground. If the angle of elevation from the ground to the kite is 0, find the length of the kite string to the nearest meter. A) 8 meters B) meters C) 8 meters D) 8 meters 9) Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. 50) 7 50) A) 5 7 ; - 7 C) ; 7 B) 8 7 ; D) 5 7 ; - 7

12 Find the trigonometric function value for the angle shown. 5) cos 5) A) cos = B) cos = 7 C) cos = 7 D) cos = 7 Determine whether the given function is positive or negative for values of t in the specified quadrant. 5) Quadrant III, sec t 5) A) Negative B) Positive Choose the point on the terminal side of. 5) = 6 A) (, - ) B) (, -) C) (-, ) D) (, -) 5) Evaluate. 5) tan ) A) B) C) D) Solve the problem. 55) A -foot ladder is leaning against the side of a building. If the ladder makes an angle of 0 with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place. A). ft B).95 ft C) 7.0 ft D).6 ft 55)

13 Find the period of the function. 56) y =.5 sin x 56) A).5 B) C) D) Solve the problem. 57) Suppose that the average monthly low temperatures for a small town are shown in the table. Month Temperature ( F) ) Model this data using f(x) = a sin(b(x - c)) + d. A) f(x) = sin x - + B) f(x) = sin 6 x - + C) f(x) = sin 6 x D) f(x) = sin 6 x - + Solve for x in the given interval. 58) sec x =, x 58) A) 6 B) 7 C) 5 D) 5 Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. 59) cos- (-0.79) 59) A).9 B) -0.8 C).89 D) 5.5 Find the exact value of the composition. 60) tan ( tan- ()) 60) A) - B) C) D) - Use the fundamental identities to find the value of the trigonometric function. 6) Find tan if cos = and sin < 0. 6) A) B) - 5 C) - D) -

14 Use basic identities to simplify the expression. 6) cot sec sin 6) A) B) csc C) sec D) tan 6) + sec cos 6) cot A) tan B) C) sec D) csc Simplify the expression. 6) -sin x - cos x 6) A) sec x - B) - C) + tan x D) 65) cos - x csc (-x) 65) A) -cot x B) - C) D) -sin x Write each expression in factored form as an algebraic expression of a single trigonometric function. 66) cos x - sin x - 66) A) (cos x + )(cos x - ) B) (cot x + )(cot x - ) C) cos x - D) sin x 67) cot x - tan x + cos x sec x 67) A) ( cot x - ) B) C) ( tan x - )( tan x + ) D) ( tan x + )(tan x + ) Find all solutions to the equation. 68) 9 sinx - 8 sin x + = -6 68) A) + n n = 0, ±, ±,... B) + n n = 0, ±, ±,... C) + n, + n n = 0, ±, ±,... D) n n = 0, ±, ±,... SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prove the identity. cot x 69) + csc x = csc x - cot x 69) 70) - sin t cos t = cos t + sin t 70) 7) cos t + sin t + + sin t = sec t 7) cos t

15 7) tan t - cot t + + cot t = tan t + - csc t tan t tan t - 7) 7) cos x sec x - - cos x sec x + = cos x tan x 7) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find an exact value. 7) sin 7) A) 6 + B) - 6 C) 6 - D) ) cos 75) A) B) 6 + C) 6 - D) Find all solutions to the equation in the interval [0, ). 76) sin x = -sin x 76) A) 8, 9 8 B) No solution C) 0,,, D),, 5, 7 Rewrite with only sin x and cos x. 77) sin x - cos x 77) A) cos x + sin x cos x - sin x + sin x cos x B) sin x cos x + cos x - cos x sinx C) sin x cos x - sin x + sin x cos x D) sin x cos x - cos x - sin x cos x 5