Practice Test - Chapter 8. Simplify each expression. SOLUTION: SOLUTION: SOLUTION: SOLUTION: SOLUTION: esolutions Manual - Powered by Cognero Page 1
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1 Simplify each expression esolutions Manual - Powered by Cognero Page 1
2 6. 9. Identify the asymptotes, domain, and range of the function graphed. Vertical asymptote: x = 2 Horizontal asymptote: esolutions Manual - Powered by Cognero Page 2
3 10. MULTIPLE CHOICE What is the equation for the vertical asymptote of the rational function A x = 2 B x = 1 There is a zero at asymptote at x = 0.. There is a vertical C x = 1 D x = 2 The degree of the numerator and denominator polynomial is one. Therefore, there is a horizontal asymptote at. Equate the denominator expression to 0 and solve for x. Draw the asymptotes, and then use the table of values to graph the function. The vertical asymptote of the rational function is x = 2. The correct choice is A. Graph each function. 11. esolutions Manual - Powered by Cognero Page 3
4 12. There is a vertical asymptote at x = 4. The degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the line y = 0. There is a zero at. There is a vertical asymptote at x = 1. Draw the asymptotes, and then use the table of values to graph the function. Since the degree of the numerator and denominator polynomials are equal, there is a horizontal asymptote at. 13. Draw the asymptotes, and then use the table of values to graph the function. esolutions Manual - Powered by Cognero Page 4
5 14. There is a zero at x = 0. There is a vertical asymptote at x = 1. Since the degree of the numerator and denominator are equal, there is a horizontal asymptote at. Draw the asymptotes, and then use the table of values to graph the function. esolutions Manual - Powered by Cognero Page 5
6 There is a zero at x = 0. There is a vertical asymptote at x = 5. Since the degree of the numerator and denominator polynomials are equal, there is a horizontal asymptote at y = 1. Therefore, the graph of graph of with a hole at x = 1. is the Draw the asymptotes, and then use the table of values to graph the function. 17. Determine the equations of any vertical asymptotes and the values of x for any holes in the graph of the function Therefore, there is a vertical asymptote at x = 7 and a hole at x = 5. esolutions Manual - Powered by Cognero Page 6
7 18. Determine the equations of any oblique asymptotes in Solve each equation or inequality. the graph of the function 19. The difference between the degree of the numerator and the degree of the denominator is 1, so there is an oblique asymptote. Divide the numerator by the denominator to determine the equation of the oblique asymptote. Check: Therefore, the equation of the oblique asymptote is. The solution is x = 5. esolutions Manual - Powered by Cognero Page 7
8 20. Divide the real line in to three intervals as shown. Test x = 2. Check: Test. Test x = 1. The solution is m = The solution of the inequality is. The excluded value for this inequality is x = 0. Solve the related equation. esolutions Manual - Powered by Cognero Page 8
9 Check: r = 3 Check: r = 2 Check: The solution is. esolutions Manual - Powered by Cognero Page 9
10 If y varies inversely as x and y = 18 when find x when y = 10. Therefore,. Check: Substitute y = 10 in the equation. 26. If m varies directly as n and m = 24 when n = 3, find n when m = 30. Substitute m = 30 in. The solution is. esolutions Manual - Powered by Cognero Page 10
11 27. Suppose r varies jointly as s and t. If s = 20 when r = 140 and t = 5, find s when r = 7 and t = BICYCLING When Susan rides her bike, the distance that she travels varies directly with the amount of time she is biking. Suppose she bikes 50 miles in 2.5 hours. At this rate, how many hours would it take her to bike 80 miles? Substitute r = 7, t = 2.5 in the relation. Substitute m = 80 in the relation. So, it would take 4 hours to bike 80 miles. 29. PAINTING Peter can paint a house in 10 hours. Melanie can paint the same house in 9 hours. How long would it take if they worked together? It would take about 4.7 hours if they worked together. esolutions Manual - Powered by Cognero Page 11
12 30. MULTIPLE CHOICE How many liters of a 25% acid solution must be added to 30 liters of an 80% acid solution to create a 50% acid solution? F 18 G 30 H 36 J What is the volume of the rectangular prism? The volume of the prism is. esolutions Manual - Powered by Cognero Page 12
Practice Test - Chapter 8. Simplify each expression. SOLUTION: SOLUTION: SOLUTION: esolutions Manual - Powered by Cognero Page 1
Simplify each expression. 1. 2. 3. esolutions Manual - Powered by Cognero Page 1 4. 5. esolutions Manual - Powered by Cognero Page 2 6. 7. esolutions Manual - Powered by Cognero Page 3 8. 9. Identify the
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