(a) What was the low temperature on July 19?

(b) When was the low temperature 73⁰ F?

(c) Is the daily low temperature a function of the date? Explain

(d) Is the date a function of daily low temperature? Explain

Table 1.5

Date in July	17	18	19	20	21	22	23
Low Temp. Fo	73	77	69	73	75	75	70

Solutions:

(a) Low temperature for July 19th is 69⁰ F.

(b) Temperature was 73⁰ F on July 17th and 20th.

(c) Yes, daily low temperature is a function of date, since for each date there is exactly one low temperature.

(d) No, date is not a function of low temperature, since there is more than one date for at least one low temperature,
example for 73⁰ F we have 2 dates, 17th and 20th.

2 - Table 1.6 shows the number of calories used per minute as a function of body weight for three sports?

(a) Determine the number of calories that a 200-lb person uses in one half-hour of
walking.

(b) Who uses more calories, a 120-lb person swimming for one hour or a 220-lb person bicycling for a half-hour?

(c) Does the number of calories used by a person walking increase or decrease as weight increases?

Table 1.6

Activity	100 lb	120 lb	150 lb	170 lb	200 lb	220 lb
Walking (3 mph)	2.7	3.2	4	4.6	5.4	5.9
Bicycling (10 mph)	5.4	6.5	8.1	9.2	10.8	11.9
Swimming (2 mph)	5.8	6.9	8.7	9.8	11.6	12.7

Solutions:

(a) According to the table, a 200-lb person uses 5.4 cal. Per min while walking. Since a half hour is 30 minutes,
a half-hour walk uses 5.4 x 30 = 162 calories

(b) A 120-lb swimmer uses 6.9 calories per minutes. Thus, in one hour the swimmer uses 6.9 x 60 = 414 calories.
A 220-lb swimmer uses 11.9 cal / min. In half hour, the bicyclist uses 11.9 x 30 = 357 calories,

Thus the swimmer uses more.

(c) Increases, since number goes from 2.7 to 5.9 in increasing values.

3 The following three tables represents the relationship between the button, N, which you push,
and the snack , S, delivered by three different vending machines.

(a) One of these vending machine is not a good one to use, because S is not a function of N,
Which one? Explain why this makes it a bad machine to use.

Machine #2, since 2 different snacks for each button - so S is not a function of N.

(b) For which vending machine(s) is S a function of N? Explain why this makes them use-friendly.

Machines # 1 and #3, give S as a function of N.

(c) For Which of the vending machines is N not a function of S? What does this mean to

the user of the vending machine?

Machine #3, N is not a function of S, e.g. When S = Snicker get N = 8 and 9.
 

Vending Machine #1     N S 1 m&ms 2 pretzels 3 dried nuts 4 Hersheys 5 Fat free cookies 6 Snickers

Vending Machine #2     N S 1 M&ms or dried fruits 2 Pretzels or Hersheys 3 Snickers or fat free cookies

Vending Machine #3     N S 1 m&ms 2 m&ms 3 pretzels 4 dried fruits 5 Hersheys 6 Hersheys 7 Fat free cookies 8 Snickers 9 Snickers

4 - Using table 1.76, sketch a graph of  , the number of gallons of paint needed to
cover a house of area A. Identify the independent and dependent variables.

Table 1.7

A	0	250	500	750	1,000	1,250	1,500
n	0	1	2	3	4	5	6

Solutions

(a) Since the number of gallons of paint needed is dependent on the area of the house,
the independent variable is area, A and the dependent variable is gallons of paint, n.

(c) n = f(A) So n = 250 A (not asked)

(b) Sketch of n (gallons) versus area (ft²):

5 (a) Which of the graphs in Figure 1.4 represent y as a function of x?
(Note that an open circle indicates a point that is not included in the graph:
a solid dot indicates a point that is included in the graph.)

All are functions except (II), (VI) and (IX) - since fail vertical line test.

(b) Which of the graphs in Figure 1.4 could represent the following situations? Give reasons.

(i) SAT Math score versus SAT Verbal score for a small number of students
(i.e. A graph of one versus the other) Graphs (V) and (VI) since need graphs at different points.

(ii) Total number of daylight hours as a function of the day of the year, shown over a period of several years. -
Need an oscillating function so (VII)

(c) Among graphs (I) - (IX) in Figure 1.4. Find tow which could give the cost of train fare as a function of time of day.
Explain the relationship between cost and time for both choices.
If train price is constant all day then (III) and if change at different times then (IV).

Figure 1.4

(I)	(II)
(III)	(IV)

(V)	(VI)
(VII)	(VIII)

(IX)

6. Consider the following stories about five different bike rides.
Match each story to one of the graphs in Figure 1.6, where d represents distance
from home and t is time in hours since the start of the ride.
(A graph may be used more than once).

(a) Starts 5 miles from home and rides 5 miles per hour away from home. (ii)

(b) Starts 5 miles from home and rides 10 mile per hour away from home. (i)

(c) Starts 10 miles from home and arrives home one hour later. (v)

(d) Starts 10 miles from home and is halfway after one hour.(iv)

(e) Starts 5 miles from home and is 10 miles from home after one hour.(ii)

Figure 1.6

(i)	(ii)	(iii)
(iv)	(v)

7. A bug starts out ten feet from a light, flies closer to the light, then further away,
then closer than before, then further away. Finally, the bug hits the bulb and flies off.
Sketch a possible graph of the distance of the bug from the light as a function of time.

Function of Bug versus distance from a light source:

Given: starts out 10 feet from source, flies closer to light, then further away,
then closer than before, then further away, and finally bug hits light source and flies off.

One possible sketch of distance of bug to light source with time is:

8. The sales tax on an item is 6%. Express the total cost, C, in terms of the price of the item, P.

Total Cost = Price + sale tax

C = P + 0.06 P = 1.06 P

So C = 1.06 P

9 Suppose that x = 5 no matter what y is.

(a) is y a function of x? Explain (b) is x a function of y? Explain

Solution:

(a)No, for there are more than one values for y for each value of x

(b) Yes, for there one value of x for each value of y

(a) y = f(x), x = 5

(b) x = f(y), x = 5

10 A person plans to leave home and walk 10 miles in total due west for a time, and then walk due north.

(a) Suppose the person will walk 10 miles in total. If w represents the (variable) distance west she walks,
and D represents her (variable) distance from home at the end of her walk, is D a function of w? Why or Why not?

Yes, since distance from home is represented by the hypotenuse of a right triangle, D,
where distance due east is, E and distance due north is N, then

(b) Suppose now that x is the distance that she walks in total. Is D a function of x? Why or why not?

No, D cannot be a function of x , since various combinations of E and N gives 10,
total distance walk, and so will give different answers for D when use Pythagorean Theorem to find distance.