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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)•
• (x, 0)
(2,1)
•
(0,y)•
• (x, 0)
(2,1)
f(x) = area of triangle
f(x) = b h2
?
x
y
?
f(x) = x y2
y = ? (in terms of x)• (2, 1)
1x – 2
f(x) = area of triangle
f(x) = b h2x
y
f(x) = x y2
1x – 2
y 1
=x
x – 2
y = x x – 2
f(x) = x •x
x – 2
2
f(x) = x2
x - 2
21
f(x) = x2 x - 2
• 12
f(x) = x2
2x – 4
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.
car A
car B
45 mph
32 mph
100 m
150 m
distance
f(x) = distance
100
150
100 – 45h
150 – 32h
distance
distance
f(x) = distance
100 – 45h
150 – 32h
distance
f(x) = distance
f(x) = (100 – 45h)2 + (150 – 32h)2
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.
revenue = price • number of units sold
revenue =
• 10,000 = $1,000,000
revenue =
• 9,900 = $1,039,500
revenue =$ 110
$100
$ 105
• 9,800 = $ 1,078,000
x = no. of $ 5 increase
revenue = (100 + 5x) (10,000 – 100x)