IMSA MI-3 2 Spring '12

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2.

IMSA

MI-3

Graph the relationship between x and y. Be sure to include the equation and various restrictions.

Problem Set 2 DUE: Tues. Jan 31 Spring '12

All answers should be exact whenever possible. Approximated answers should be rounded to four significant digits unless otherwise stated in the problem.

1. A group of 4 friends went to a restaurant for dinner. They told the waiter that they wanted to split the bill evenly. When the waiter collected from them he discovered that they each would get back $2.50 because he had mistakenly divided the bill by 3 instead of 4. How much was the original bill?

2x - 8 y + 4

Perimeter = 20

3. Sketch: a)

x

y

4 and b)

x

y

4

4.

[Label important features.]

Answer: A(lways), S(ometimes), N(ever). If your answer is S(ometimes), give an example

where the statement is true and an example where the statement is false. If your answer is

A(lways) or N(ever), give a reason for your answer. a)

x

= x d)

x

< x b)

x

= –x e)

x

2

= –x c)

x

2

=

x

f)

x

5. d)

x

2

= –x e)

6. a. b. c.

x

2

3

x

4 and

Write a simplified form of

f

Compute

g f

(2)

3

x

2

For what values of x is f(x) < g(x)?

.

x

PS 2.1

2

= x

> x

Give the domain over which each statement is true: a) | x | = x b) | x | < x c) f)

| x | = –x

| x | > x

Rev. S12

7. Graph each function and label at least 3 specific points, including intercepts and other important

points. Give the domain and range. a.

x

3 b.

0.5(

x

3)

2

6

x

c. d.

 

3

x

(Careful!)

8. Let

P

(

x

,

y

) be a point such that

P

(

x, y

) =

y t t

2 –1

Note: These are called

parametric equations,

where

t

is the

parameter.

You can enter this on your TI-89 by changing MODE to "parametric." Your "Y=" menu will now receive

t

as the variable. Enter the restrictions on

t

under "Window." a) Graph

P

for –4 ≤

t

≤ 3. (Label key points) b) Write

x

as a function of

y

. (Give restrictions on

y

.)

9. The local Family Restaurant has a daily breakfast special in which the customer may

choose one item from each of the following groups:

Breakfast Sandwich Accompaniments Juice

egg and ham egg and bacon egg and cheese

breakfast potatoes apple slices fresh fruit cup pastry

orange cranberry tomato apple grape

a.) How many different breakfast specials are possible?

b.) How many different breakfast specials without meat are possible?

10. In calculus it is often handy to have exponential functions written as a power of

e

. The half life formula states:

A t

A

0

1

 

t h

where

A t

is amount after time

t

,

A

0

is initial amount,

h

is the half life, and

t

is time. So if a substance has a half life of 3.6 hr, we get

A t

A

0

1

 

t

3.6

. Convert this formula to one in which the base is

e

and not

1

2 exponent approximation.

. Give answer to three decimal places in your

PS 2.2 Rev. S12

11. Solve the equations: a) log

 b) log3

x

3

2

 

= log

= log2 [Note: log2(A) is shorthand for (log A)2]

12. Determine the inverse of each of the following: a)

4 log ( )

2

x

b)

5

3

x

4

13.

If a red six-sided die and a blue six-sided die are tossed, what is the probability that, a) the red comes up with a ‘6’ and the blue with an even number? b) c) that one comes up with a ‘6’ and the other with an even number? that the sum is 10?

PS 2.3 Rev. S12

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