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TO THE BOARD!!! (Chapter 5 Review Game)

TO THE BOARD!!! (Chapter 5 Review Game). Gurjeet, Anika, Massuma, Amarpal. For the function f(x) = 7x-m / 2 – nx Find the values of m and n, such that the vertical asymptote is at x=6 and the x-int is 5. Answer: Denominator: 2-nx = 0 2-n(6)= 0 -6n = -2 n = 2/6 n = 1/3

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TO THE BOARD!!! (Chapter 5 Review Game)

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  1. TO THE BOARD!!! (Chapter 5 Review Game) Gurjeet, Anika, Massuma, Amarpal

  2. For the function f(x) = 7x-m / 2 – nx Find the values of m and n, such that the vertical asymptote is at x=6 and the x-int is 5

  3. Answer: Denominator: 2-nx = 0 2-n(6)= 0 -6n = -2 n = 2/6 n = 1/3 Sub x=5 and n=1/3 into equation to solve for m 7(5) – m / 2-(1/3)(5) = 0 35 – m = 0 -35 = m

  4. Find the instantaneous rate of change, when x = 4

  5. Answer: IROC = -1.3  use IROC formula : f(a=h) – f(a) / h

  6. Mark takes x minutes to deliver newspapers, and Joe takes x-13 minutes. When they work together, they can deliver newspapers to the entire neighbourhood in 42 minutes. How long does it take Mark to deliver newspapers alone?

  7. Answer: x > 13 (1/ x) + (1/x-13) = 1/42 (1/ x) + (1/x-13) - 1/42 = 0 [ (x-13+x) / x*(x-13) ] – 1/42 = 0 x2-97x+546 = 0 (x-6)(x-91) x > 13, so 6 is inadmissible So x = 91 It will take Mark 91 minutes to deliver the papers alone.

  8. Determine: Domain, Range, Intercepts, and Asymptotes for the function: f(x) = x-2 / 2x-1

  9. Answer: D: {x є R} X-intercept: x= 2 Y-intercept: y = 2 VA: x = ½ HA: y = ½

  10. Sketch the graph of the function: y= 1/ 2x

  11. Answer:

  12. The concentration, c, of a drug in the bloodstream t hours after the drug was taken orally is given by • where c is measured in milligrams per litre. • Calculate that average rate of change in the drug’s concentration during the first 2 h since ingestion. • Estimate the rate at which the concentration of the drug is changing after exactly 3 h.

  13. Answer: • 0.455 mg/L • b) -0.04 mg/L

  14. Solve the equation algebraically: x + (x/x-2) = 0

  15. Answer: x + (x/x-2) = 0 x2-2x+x / (x-2) = 0 x2-x / (x-2) = 0 x(x-1) / (x-2) = 0 Roots: 0, 1 VA: x = 2

  16. Solve the inequality : x/(x+9) ≥ 1/(x+1)

  17. Answer: x/(x+9) ≥ 1/(x+1) x2-9 / (x+9)(x+1) ≥ 0 (x+3)(x-3) / (x+9)(x+1) ≥ 0 VA: x= -9 , -1 Roots: x = 3, -3 THEN: Use factor table to find the intervals where the x values are ≥ 0 x E (-∞, -9), [-3, -1), [3, ∞)

  18. Communication Question: Explain the steps needed to graph a reciprocal function using the graph of the original function

  19. Answer: • Determine the zeroes of the original function  these will be the asymptotes of the reciprocal • Determine the +/- intervals  these will be the same on the reciprocal graph • Determine intervals of increase/decrease  these will be the opposite on the reciprocal graph

  20. Write an equation for a rational function with the following properties: • Hole at x = -2 • VA at x = 1

  21. Answer: y = x2-4 / x2+3x+2

  22. Determine the instantaneous rate of change and the value of x at which there is an undefined instantaneous rate of change. where x = 2

  23. Answer: IROC = 286.1 Undefined at x = -3/2 (-1.5)

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