Math Analysis Midterm Review. Directions: This assignment is due at the beginning of class on Friday, January 9th

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1 Math Analysis Midterm Review Name Directions: This assignment is due at the beginning of class on Friday, January 9th This homework is intended to help you prepare for the midterm exam. The questions are of roughly the same level of difficulty as those that will appear on the exam, and solving them will require you to review key concepts that are likely to be tested. If you need additional work space, use notebook paper and attach it to this packet. This assignment is a measure of your ability to apply your knowledge. It is to be completed individually using only your class notes, textbook, calculator, and handouts. Any questions regarding the assignment should be directed to Mrs. Becker afterschool or glorybeth_becker@hcpss.org. I will be checking my during the break and available afterschool (to be announced) during the first week of January. Please read and sign the statement below. I affirm that I completed this assignment by myself using only my notes, handouts, calculator, and textbook. Furthermore, I affirm that I discussed this assignment with no one any questions I had regarding this assignment were directed to Mrs. Becker Signature: Date: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation. ) 5x + 9 = x + 4 ) A) - 5 B) , - 5 C) 6 4, D) 6 ) (x - ) + + = 9 ) A) {- 4, } B) - 9 C) - 9, 5 D) Evaluate the series, if it converges. ) ) A) B) 4 5 C) 6 5 D) Does not converge 4) 5 i= A) 5 i - B) 55 4) C) 9 D) Does not converge.

2 Write an equation that results in the indicated translation. 5) The square root function, shifted 7 units to the left 5) A) y = x + 7 B) y = x - 7 C) y = x - 7 D) y = x + 7 6) The squaring function, shifted 4 units upward 6) A) y = x B) y = x + 4 C) y = x - 4 D) y = 4x 4 Evaluate the sum. Round to the nearest hundredth, if necessary. 7) 5 (i - ) 7) i= A) B) 0 C) 8 D) 6 8) 4 k= k 8) A) 0 B) 8 C) 6 D) Find the requested composition or operation. 9) f(x) = 4x + x + 8, g(x) = x - 5 Find (g f)(x). A) 4x + x + B) 8x + 4x + C) 4x + 4x + D) 8x + 4x + 9) Determine if the graph is symmetric with respect to the x-axis, y-axis, or origin. 0) 0) A) No symmetry B) Origin C) y-axis D) x-axis Find a general term an for the geometric sequence. ) 4, 4, 4 9, 4,... ) 7 A) an = 4-8 (n - ) B) a n = 4n C) an = 4 + (n - ) D) a n = 4 n -

3 ), -,, - 4,,... ) 8 A) an = n- B) an = 6-4 n- C) an = - n- D) an = - n- Find the sum of the arithmetic series using a formula. ) The first 46 terms of the series whose terms are an = 0-4n ) A) -764 B) C) -864 D) ) ) A) 9600 B) 970 C) 9480 D) 9,68 Find the requested value. 5) 5x + if x < f(-) for f(x) = x if x 7-7x if x > 7 A) -4 B) 6 C) 4 D) -9 6) f(0) for f(x) = x - 9 if x < 7 - x if x A) 4 B) -6 C) 7 D) -9 5) 6) Find the specified domain. 7) For f(x) = x - 5 and g(x) = x + 9, what is the domain of f g? 7) A) (-9, 9) B) (-9, ) C) [0, ) D) [9, ) 8) For g(x) = x + 4 and h(x) =, what is the domain of (h g)? 8) x - 8 A) [-4, 8) (8, ) B) [-4, 60) (60, ) C) [0, 60) (60, ) D) [0, 8) (8, ) 9) For f(x) = x - 5 and g(x) = x +, what is the domain of (f + g)? 9) A) [0, ) B) (-, ) C) [, ) D) [-, ) Provide an appropriate response. 0) Which of the following is a horizontal translation of the function y = [[x]]? 0) A) y = [[x]] - B) y = [[x]] C) y = [[x - ]] D) y = -[[x]] ) Consider the sequence defined by an = -8n Is this sequence arithmetic, geometric, or neither? ) A) Arithmetic B) Geometric C) Neither

4 ) Explain how the graph of g(x) = f(x) - 9 is obtained from the graph of y = f(x). ) A) Shift the graph of f to the left 9 units. B) Shift the graph of f upward 9 units. C) Shift the graph of f to the right 9 units. D) Shift the graph of f downward 9 units. ) Which function represents a vertical translation of the parabola y = (x - ) + 5? ) A) y = x + 5 B) y = (x + ) + 5 C) y = (x - ) + 6 D) y = -(x - ) + 5 4) The sum of an infinite geometric series exists if: 4) A) r < B) r C) r > D) r Write the first n terms of the given arithmetic sequence (the value of n is indicated in the question). 5) a = 4, d = -5, n = 5 5) A) 9, 4, -, -6, - B) 4, 9,, -, -6 C) 9, 4, 9, 4, - D) 4, 9, 4, -, -6 Find the indicated term of the geometric sequence. 6) a = 4, r =, n = 5 6) A) a5 = 8 B) a5 = 5 C) a5 = D) a5 = 64 Evaluate the sum. 7) (i + ) 7) i= A) 76 B) 88 C) 77 D) 87 Perform the requested composition or operation. 8) Find (f g)(8) when f(x) = -4x - 5 and g(x) = -4x + 5x +. 8) A) -4 B) -49 C) 847 D) ) Find (f - g)(-4) when f(x) = -x + 7 and g(x) = x +. 9) A) 45 B) -8 C) -46 D) -6 Determine the intervals on which the function is increasing, decreasing, and constant. 0) 0) A) Increasing on (-, 0]; Decreasing on [0, ) B) Increasing on [0, ); Decreasing on (-, 0] C) Increasing on (-, ) D) Decreasing on (-, ) 4

5 f(x + h) - f(x) Determine the difference quotient (h 0) for the function f. Simplify completely. h ) f(x) = x + x - ) A) 6xh + h + h B) x h C) 6x + D) 6x + + h Find a formula for the nth term of the arithmetic sequence shown in the graph. ) ) A) an = n - B) an = n + C) an = n + D) an = - n Solve the inequality. ) 7x < 9 ) A) -, C) -, , D) 7 B) - 0 7, Use the tables to evaluate the expression if possible. 4) Find (g f)(). 4) x 7 9 f(x) 49 8 x g(x) A) 67 B) 8 C) 07 D) 89 Determine whether the function is even, odd, or neither. 5) f(x) = x4 + 4x - 5) A) Even B) Odd C) Neither 6) f(x) = -4x5-5x 6) A) Even B) Odd C) Neither 5

6 Find the common ratio r for the given infinite geometric sequence. 7) 4, 8, 6,, 64,... 7) A) 6 B) C) 4 D) Use the formula for Sn to find the sum of the first five terms of the geometric sequence. Round to the nearest hundredth, if necessary. 8),, 4, 8,... 8) A) - 48 B) 9 C) 6 D) 4 Write the equation that results in the desired transformation. 9) The square root function, reflected across the x-axis 9) A) y = - x B) y = x - C) y = -x D) y = x 40) The squaring function, vertically stretched by a factor of 6 and reflected across the x-axis 40) A) y = 6(x - 6)x B) y = 6x C) y = (x - 6) D) y = -6x Find the first term and the common difference for the arithmetic sequence. 4) a = 45, a 56 = 5 4) A) a = 700, d = 5 B) a = 5, d = 0 C) a = 5, d = 700 D) a = 700, d = 0 4) S5 = 70, a5 = 6 4) A) a =, d = 6 B) a = -0, d = 6 C) a =, d = 0.4 D) a = -0, d = 0.4 Find the first six terms of the sequence. 4) a = -, an = an ) A) 7, 6, 5, 4, 4, 5 B) -, 7, 6, 5, 4, 4 C) -, 9, 8, 7, 6, 45 D) 0, 9, 8, 7, 6, 45 Write out the first five terms of the sequence. 44) an = 6n - n + 6n A) 5 7, 6, 7 7, 40, 9 55 C), 6, 9 7, 5 8, 55 B) 5 7, 0, 7 5,, 9 D) 5 6,, 7 8, 4, ) 6

7 45) an = n 45) A), 4, 9, 6, 5 C) 4, 9, 6, 4 5, 5 6 B),,, 4, 5 D), 4,, 6, 5 Give the equation of the function whose graph is described. 46) The graph of y = x is shifted units to the left. This graph is then vertically shrunk by a factor of 6 46) and reflected across the x-axis. Finally, the graph is shifted 8 units downward. A) y = 6 (x - ) - 8 B) y = - 6 (x - ) + 8 C) y = - 6 (x - ) - 8 D) y = - 6 (x + ) - 8 Find the sum of the geometric series. 47) 5 4 () k 47) k= A) 48 B) C) 57 D) 7 Determine the intervals of the domain over which the function is continuous. 48) 48) A) (-, 4); (4, ) B) (-, ); (, ) C) (-, ) D) (-, -); (-, ) Solve the problem. 49) Find the sum of all the integers from to ) A) 05 B) 068 C) 979 D) 0 Write the sum of the geometric series as a rational number. 50) ) A) B) C) D)