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(0,y)

1. A triangle is bounded by the x-axis, y-axis and the line that passes through the point (2,1) with x-intercept at (x,0) and y-intercept at (0,y). Express the area of the triangle as a function of x. (0,y). •. (2,1). •. (x, 0). •. f(x) = area of triangle. (0,y). •. f(x) = b h. (2,1).

benedict-levine
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(0,y)

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  1. 1. A triangle is bounded by the x-axis, y-axis and the line that passes through the point (2,1) with x-intercept at (x,0) and y-intercept at (0,y). Express the area of the triangle as a function of x. (0,y) • (2,1) • (x, 0) •

  2. f(x) = area of triangle (0,y) • f(x) = b h (2,1) ? • 2 (x, 0) • ? f(x) = x y 2 y = ? (in terms of x) y • (2, 1) x 1 x – 2

  3. f(x) = area of triangle y f(x) = b h x 2 1 f(x) = x y x – 2 2 x y f(x) = x • x x – 2 = x – 2 1 2 y = x x – 2

  4. x2 f(x) = x - 2 2 1 f(x) = x2 1 • x - 2 2 x2 f(x) = 2x – 4

  5. 2. Two cars are both approaching an intersection. Car A is traveling at 45 mph and is presently 100 miles from the intersection while car B is running at 32 mph and is 150 miles from the intersection. Express the distance between the two cars as a function of time in hours, h.

  6. f(x) = distance car A 45 mph distance 100 m 150 m car B 32 mph

  7. distance 100 150 f(x) = distance distance 100 – 45h 150 – 32h

  8. f(x) = distance f(x) = (100 – 45h)2 + (150 – 32h)2 distance 100 – 45h 150 – 32h

  9. 3. The CEO of a certain company that manufactures calculators noticed that when a calculator was sold at $100 each, a total of 10,000 calculators were sold in a month. He also noticed that for every $5 increase in the price of the calculator, there was a decrease of a 100 pieces of it being bought. Express the revenue of the company as a function of the number of $5 increase in price.

  10. number of units sold price • revenue = revenue = $100 • 10,000 = $1,000,000 revenue = $ 105 • 9,900 = $1,039,500 revenue = $ 110 • 9,800 = $ 1,078,000 x = no. of $ 5 increase revenue = (100 + 5x) (10,000 – 100x)

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