Suppose a company makes two products. Let x represent
the number of the first product made and y represent the number of the
second product made. If the first product makes $2 each and the
second $3 each,
the profit function would be:

P(x, y) = 2x + 3y

Notice that profit is a function of two variables.
There are a few ways we could graph this function. One way is to
graph in a three dimensional plane. We will talk about this later
in the year. Another way to graph this function is to hold one of
the variables constant. For example, we could hold y constant
like: y = 2, or y = 3 or y = 4, etc. The equations would look
like:

P(x, 2) = 2x + 6

P(x, 3) = 2x + 9

P(x, 4) = 2x + 12

These graphs all have the same slope but different
y-intercepts. These make a family of curves. They will be
graphed in the xP plane.

Another way we can graph this is by holding the profit
constant. For example, we could let P = 6 or P = 12 or P =
18. Then the equations would be:

6 = 2x + 3y

12 = 2x + 3y

18 = 2x + 3y

Another equation we could use is:

d(r, t) = rt

Suppose we hold t constant at t = 1, t = 2 and t = 3.
Make a graph of these three equations:

d(r, 1) = r

d(r, 2) = 2r

d(r, 3) = 3r

Now graph the same function holding the distance constant at
d = 10, d = 20,

and d = 30. The equations are

10 = rt

20 = rt

30 = rt

I'm ready for that practice test now!

I'm almost ready. I think I will go back and
review!

Current quizaroo #
4b

1) y + 3 = -f(x - 1) Describe the
translations, symmetry and stretching/shrinking for this graph:

a)
Reflected about the y-axis, moved three units up and one unit to the
left

b)
Reflected about the y-axis, moved three units down and one unit to the
right

c)
Reflected about the x-axis, moved three units up and one unit to the
left

d)
Reflected about the x-axis, moved three units down and one unit to the
right

e)
Moved three units down and one unit to the right

2) Write the equation of a
function that is shifted 2 units up and 4 units to the left, that is
reflected about the x-axis with a stretch vertical factor of 2.

a) y - 2 = -2f(x
+ 4)

b) y + 2 = -2f(x - 4)

c)
y - 2 = 2f(x + 4)

d)
y + 2 = 2f(x - 4)

e)
y +4 = -2f(x - 2)

3) Find the inverse function to the equation: y
= -3x
+ 4

a)
y = 3x - 4

b)
y = (4 - x)/3

c)
y = (x - 4)/3

d)
y = (x + 3)/4

e)
y = (3 - x)/4

4) If g(x) = x^{2} - 2, x < 0, find the inverse function.

____

a) y = -\/ x + 2, x > -2

____

b) y = \/ x + 2, x > -2

c) y = x + 2, x > -2

d) y = -(x + 2), x > -2

e) doesn't have an inverse function, because it
doesn't pass
the horizontal line test

5) Name an
ordered pair that is not in the domain of f(a, b) = (a - b)/(a +
b)