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You may solve a set of 10 questions with their detailed solutions and also a set of 50 questions, with their answers, in the applet to self test you background on how to

- Solve linear equations.
- Simplify algebraic expressions.
- Simplify absolute value expressions.
- Find the distance between two points.
- Find x intercept(s) of the graph of an equation.

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30 Algerba questions with showing work. Questions on PDF attached

30 Algerba questions with showing work. Questions on PDF attached

Problems #1–12 are Multiple Choice.Problems #13–21 are Short Answer. (Work not required to be shown)Problems #22–30 are Short Answer with work required to be shown.MULTIPLE CHOICE1. Determine the domain and range of the piecewise function. 1. ______A. Domain [– 2, 4]; Range [– 2, 1]B. Domain [– 2, 4]; Range [– 4 , 2]C. Domain [– 4, 2]; Range [– 2, 4]D. Domain [0, 2]; Range [– 2, 0]2. Solve: 15 + 2x = − x 2. ______A. –3B. –3, 5C. –1/5D. No solution-4 -2 2 4-2-424College Algebra MATH 107 Fall, 2017, V3.2Page 2 of 113. Determine the interval(s) on which the function is decreasing. 3. ______A. (−¥,−1) and (1,3)B. (−5/ 3, 0) and (2,11/ 3)C. (−1,1) and (3,¥)D. (− 4 / 3, 1)4. Determine whether the graph of 3 y = x is symmetric with respect to the origin,the x-axis, or the y-axis. 4. ______A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, andnot symmetric with respect to the originB. symmetric with respect to the x-axis onlyC. symmetric with respect to the y-axis onlyD. symmetric with respect to the origin only5. Solve, and express the answer in interval notation: | 7 – 5x | £ 8. 5. ______A. (–¥, –1/5]B. (–¥, –1/5] È [3, ¥)C. [– 1/5, 3]D. [– 1/5, ¥)College Algebra MATH 107 Fall, 2017, V3.2Page 3 of 116. Which of the following represents the graph of 9x − 4y = 36 ? 6. ______A. B.C. D.College Algebra MATH 107 Fall, 2017, V3.2Page 4 of 117. Write a slope-intercept equation for a line parallel to the line x – 7y = 3 which passes throughthe point (28, –5). 7. ______A.197y = x −B.157y = x −C. y = −7x +191D.117y = − x −8. Which of the following best describes the graph? 8. ______A. It is the graph of a function and it is one-to-one.B. It is the graph of a function but not one-to-one.C. It is the graph of an absolute value relation.D. It is not the graph of a function.College Algebra MATH 107 Fall, 2017, V3.2Page 5 of 119. Express as an equivalent expression: 2 log (x + 3) – 4 log y + log 1 9. ______A. log (2x + 7 − 4y)B.6log( )log(4 )xyC.249logxy + D.( )243logxy + 10. Which of the functions corresponds to the graph? 10. ______A. ( ) 2 1 x f x e− = −B. ( ) 1 x f x e− = +C. ( ) 2 x f x = −e +D. ( ) 2 x f x e− = +College Algebra MATH 107 Fall, 2017, V3.2Page 6 of 1111. Suppose that for a function f , the equation f (x) = 0 has no real-number solutions.Which of the following statements MUST be true? 11. ______A. f (x) > 0 for all x in the domain of f.B. f is an invertible function.C. f has no x-intercepts.D. f has no y-intercepts.12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (Noformulas are given.) What is the relationship between g(x) and f (x)?12. ______y = f (x) y = g(x)A. g(x) = f (x – 3) – 2B. g(x) = f (x – 2) – 3C. g(x) = f (x + 3) – 2D. g(x) = f (x + 2) – 32 -4 -2 4-2-424-4 -2 2 4-2-424College Algebra MATH 107 Fall, 2017, V3.2Page 7 of 11SHORT ANSWER:13. Multiply and simplify: (8 + i)(5 + 3i).Write the answer in the form a + bi, where a and b are real numbers. Answer: ________14. Solve, and write the answer in interval notation:205xx+£−. Answer: ________15. A can of soda at 78° F. is placed in a refrigerator that maintains a constant temperature of 35°F. The temperature T of the soda t minutes after it is placed in the refrigerator is given byT(t) = 35 + 43e– 0.058 tFind the temperature of the soda 12 minutes after it is placed in the refrigerator. (Round to thenearest tenth of a degree.)Answer: ________16. Find the value of the logarithm: 51log125 . Answer: ________17. Solve: 38x−5 = 9. Answer: ________18. Suppose $3,400 is invested in an account at an annual interest rate of 6.1% compoundedcontinuously. How long (to the nearest tenth of a year) will it take the investment to double insize? Answer: ________19. Let f (x) = x2 + 8x + 19.(a) Find the vertex. Answer: ________(b) State the range of the function. Answer: ________(c) On what interval is the function increasing? Answer: ________College Algebra MATH 107 Fall, 2017, V3.2Page 8 of 1120. Consider the polynomial P(x), shown in both standard form and factored form.P(x) = x3 − 3x2 − x + 3 = (x +1)(x −1)(x − 3)(a) Which sketch illustrates the end behavior of the polynomial function?Answer: ________(b) State the y-intercept. Answer: ________________(c) State the zeros of the function. Answer: ________________(d) State which graph below is the graph of P(x). Answer: ________GRAPH A GRAPH BGRAPH C GRAPH DA.B. C. D.vvvvvvvvvvvv vvvvCollege Algebra MATH 107 Fall, 2017, V3.2Page 9 of 1121. Let2( )3xf xx+=−.(a) State the domain. Answer: _________________(b) State the vertical asymptote(s). Answer: _________________(c) State the horizontal asymptote. Answer: _________________(d) Which of the following represents the graph of2( )3xf xx+=−? Answer: ______________GRAPH A. GRAPH B.GRAPH C. GRAPH D.College Algebra MATH 107 Fall, 2017, V3.2Page 10 of 11SHORT ANSWER, with work required to be shown, as indicated.22. Let f (x) = x – 3 and g(x) = x + 5 .(a) Find ) 1 (− gf. Show work.(b) Find the domain of the quotient functiongf. Explain.23. Points (1, –5) and (9, –1) are endpoints of the diameter of a circle.(a) What is the length of the diameter? Give the exact answer, simplified as much as possible.Show work.(b) What is the center point C of the circle?(c) Given the point C you found in part (b), state the point symmetric to C about the x-axis.24. Find the equation for a line which passes through the points (4, 3) and (6, –7). Write theequation in slope-intercept form. Show work.25. A salesperson earns a base salary of $2,100 per month and a commission of 6.5% on theamount of sales made. If the salesperson has a paycheck of $5,168 for one month, what was theamount of sales for the month? Show work.26. Let f (x) = 3x2 + 8 and g(x) = x – 4.(a) Find the composite function ( f o g)(x) and simplify. Show work.(b) Find ( f o g ) (−1) . Show work.27. Find the exact solutions and simplify as much as possible: 8x2= 3 + 8x. Show work.28. Given the function1( ) 59f x = − x , find a formula for the inverse function. Show work.College Algebra MATH 107 Fall, 2017, V3.2Page 11 of 1129. The Adventure Travel bus company has determined that when x tourists are given aparticular bus tour, the profit P (in dollars) is given byP(x) = –0.25 x2 + 25.50x – 220(a) What is the company’s profit if 32 tourists are given the tour?(b) How many tourists should be given the tour in order to maximize the company’s profit?Show work.30. Solve: 25 1202 4xx x++ =+ −. Show work.

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