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What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

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Presentation transcript:

FRIDAY You need a CALCULATOR Use your own or check one out with your ID or cell phone Pickup WS 1-3

Warm-up Given relation: {(2, -3), (4, 1), (-5, -3), (-1, 1)} Domain: Range: Is it a function? Yes/ No Are these 2 graphs functions?

Warm-up Given relation: {(2, -3), (4, 1), (-5, -3), (-1, 1)} Domain: {-5, -1, 2, 4} Range: {-3, 1} Is it a function? Yes/ No

Announcements TODAY ends the 2 nd week of this 5 week grading period TODAY is the last day to makeup Unit 1 Quiz #1 Mini Quiz Tuesday

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

Objectives I can recognize and solve direct and inverse variation word problems. I can determine which graph models each type of variation

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)

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 Recipes Paint Mixtures

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

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

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

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?

Your TURN #1 on Homework Find y when x = 6, if y varies directly as x and y = 8 when x = 2.

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

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

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 Pressure versus Volume

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

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

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.

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

Direct vs. Inverse Variation

Homework WS 1-3 (answers on website) Mini Quiz next class