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Warm-up

Warm-up. Given this relation: {(2, -3), (4, 1), (-5, -3), (-1, 1) Domain: Range: Is it a function? Yes/ No Given the graph on the right Domain (INQ) Domain (INT) Range (INQ) Range (INT). Warm-up. Given this relation: {(2, -3), (4, 1), (-5, -3), (-1, 1) Domain: {-5, -1, 2, 4}

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Warm-up

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  1. Warm-up • Given this relation: {(2, -3), (4, 1), (-5, -3), (-1, 1) • Domain: • Range: • Is it a function? Yes/ No • Given the graph on the right • Domain (INQ) • Domain (INT) • Range (INQ) • Range (INT)

  2. Warm-up • Given this relation: {(2, -3), (4, 1), (-5, -3), (-1, 1) • Domain: {-5, -1, 2, 4} • Range: {-3, 1} • Is it a function? Yes/ No • Given the graph on the right • Domain (INQ): x ≤ 2 • Domain (INT): (-∞, 2] • Range (INQ): y ≤ 0 • Range (INT): (-∞, 0]

  3. Sections 2-5 & 8-1 Direct & Inverse Variations

  4. Objectives • I can recognize and solve direct variation word problems. • I can recognize and solve inverse variation word problems

  5. Direct Variation As one variable increases, the other must also increase ( up, up) OR As one variable decreases, the other variable must also decrease. (down, down)

  6. Real life? • With a shoulder partner take a few minutes to brainstorm real life examples of direct variation. Write them down. Food intake/weight Exercise/weight loss Study time/ grades Hourly rate/paycheck size Stress level/blood pressure

  7. Direct Variation • y = kx • k is the constant of variation • the graph must go through the origin (0,0) and must be linear!!

  8. Direct Variation Ex 1)If y varies directly as x and y = 12 when x = 3, find y when x = 10.

  9. FIRST: Find your data points! (x,y) NEXT: Solve for k & write your equation LAST: use your “unknown” data point to solve for the missing variable. Solving Method #1 Use y=kx

  10. FIRST: Find your data points! (x,y) NEXT: substitute your values correctly LAST: cross multiply to solve for missing variable. Solving Method #2

  11. FIRST: Find your data points! (x,y) FIRST: Find your data points! (x,y) NEXT: substitute your values correctly NEXT: Solve for k & write your equation LAST: use your “unknown” data point to solve for the missing variable. LAST: cross multiply to solve for missing variable. What did we do? Use y=kx EITHER ONE WILL WORK!! ITS YOUR CHOICE!

  12. Direct Variation Application Ex: In scuba diving the time (t) it takes a diver to ascend safely to the surface varies directly with the depth (d) of the dive. It takes a minimum of 3 minutes from a safe ascent from 12 feet. Write an equation that relates depth (d) and time (t). Then determine the minimum time for a safe ascent from 1000 feet?

  13. Your TURN #3 on Homework • Find y when x = 6, if y varies directly as x and y = 8 when x = 2.

  14. Inverse Variation As one variable increases, the other decreases. (or vice versa)

  15. Inverse Variation • This is a NON-LINEAR function (it doesn’t look like y=mx+b) • It doesn’t even get close to (0, 0) • k is still the constant of variation

  16. Real life? • With a shoulder partner take a few minutes to brainstorm real life examples of inverse variation. Write them down. Driving speed and time Driving speed and gallons of gas in tank

  17. Inverse Variation Ex 3) Find y when x = 15, if y varies inversely as x and when y = 12, x = 10.

  18. FIRST: Find your data points! (x,y) NEXT: Find the missing constant, k,by using the full set of data given LAST: Using the formula and constant, k, find the missing value in the problem Solving Inverse Variation

  19. FIRST: Find your data points! (x,y) NEXT: substitute your values correctly LAST: use algebra to solve for missing variable. Method #2

  20. FIRST: Find your data points! (x,y) FIRST: Find your data points! (x,y) NEXT: Find the missing constant, k,by using the full set of data given NEXT: substitute your values correctly LAST: Using the formula and constant, k, find the missing value in the problem LAST: use algebra to solve for missing variable. What did we do? EITHER ONE WILL WORK!! ITS YOUR CHOICE!

  21. Inverse Variation Application Ex:The intensity of a light “I” received from a source varies inversely with the distance “d” from the source. If the light intensity is 10 ft-candles at 21 feet, what is the light intensity at 12 feet? Write your equation first.

  22. Your TURN #7 on Homework Find x when y = 5, if y varies inversely as x and x = 6 when y = -18.

  23. Direct vs. Inverse Variation

  24. Homework • WS 1-7 • Quiz next class

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