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)