Section 1.2
1.
Yes it is a function. It passes the vertical line test.
2.
No it is not a function. It fails the vertical line test.
3.
Yes it is a function. It passes the vertical line test.

4-7
a.Evaluate the given expression
b.Find the domain of the function
c.Find the range
(hint: use a graphing calculator)
4.
f (x)  x 1
Find f (10)
b. The domain is determined by the square root. The quantity inside the
root sign must not be negative so x – 1 ≥ 0 or x ≥ 1.
c. Range from a calculator y ≥ 0.

5.
1
h(z) 
z4
, find
h(5)

b. Find the domain. The problem is that the function includes division so we must
make sure we are not dividing by 0. z + 4 ≠ 0 or z ≠ - 4.
c. The range from a calculator is y ≠ 0.
6.

h(x)  x1/ 4
, find
h(81)

b. Find the domain. The problem is that the function includes an even rood
so we must make sure that the base is not negative and since the base in x
then x ≥ 0.
c. The range from a calculator is y ≥ 0.
7.

f (x)  4  x 2 , find
f (0)


OR use your calculator.
From calculator.
8-9 Graph each function.
8.

f (x)  3x 2
9.

f (x)  2x 2  4 x 16
10
a. Graph the function in an appropriate window. (answers may vary)
b. Find the vertex.
f (x)  x 2  40x  500
a.

My window is - 60 ≤ x ≤ 10 and -100 ≤ y ≤ 1000
b. Using a calculator and minimum V (- 20, 100).

11 – 15 Solve each equation by factoring, completing the square, using your
calculator or the Quadratic formula, as you wish.
11.
x 2  6x  7  0
12.

2x 2  40  18x
13.

2x 2  50  0

14.
4 x 2 12x  8
15.

3x 2 12  0
16-18 Solve each equation using a graphing calculator
16.
x 2  x  20  0

My window is - 5 ≤ x ≤ 6 and -22 ≤ y ≤ 6
17.
4 x 2  24 x  45  9

My window is - 7 ≤ x ≤ 1 and - 2 ≤ y ≤ 16
18.
2x 2  3x  6  0

My window is - 4 ≤ x ≤ 3 and -9 ≤ y ≤ 15
19. Business: Cost Functions A lumberyard will deliver wood for $4 per board foot
plus a delivery charge of $20. Find a function C (x) for the cost of having x board feet
of lumber delivered.
The unit cost is $4 per board feet and the fixed cost is the delivery charge of $20. Let
x be the number of board feet then the cost C
C (x) = 4x + 20
20. Business: salary An employee’s weekly salary is $500 plus $15 per hour of overtime.
Find a function P(x) giving his pay for a week in which he worked x hours of overtime.
The overtime salary is $15 per hour and the fixed salary is $500. Let x be the
number of overtime hours then the total pay will be the fixed pay plus the overtime
pay of
P(x) = 500 + 15x
21. General: Water Pressure At a depth of d feet underwater, the water pressure is
p (d) = 0.45 d + 15 pounds per square inch. Find the pressure at:
a. The bottom of a 6-foot-deep swimming pool.
b. The maximum ocean depth of 35,000 feet.
22. General: Stopping Distance A car traveling at speed v miles per hour on a dry road
should be able to come to a full stop in a distance of
D(v)  0.055v 2 1.1v feet
find the stopping distance required for a car traveling at:
40 mph

23. Biomedical: Cell Growth The number of cells in a culture after t days is given
by N(t)  200  50t 2 . Find the size of the culture after
a. 2 days
b. 10 days
24. Business: Break-Even Points and Maximum Profits A company that produces tracking
devices for computer disks drives finds that if it produces x devices per week, its costs
and its revenue (both in dollars) will be as follows:
c(x)  180x 16000
R(x)  2x 2  660x
a. Find the company’s break-even points.
b. Find the number of devices that will maximize profit, and the maximum profit.
a.
 graph
To find the break-even points
the functions on your calculator and
use the intersect function.
(40, 23200) and (200, 52000)
b. To find the maximum profit graph the
profit function P(x) = R(x) – c(x) and find its
vertex. The maximum profit of $12,800
occurs at x = 120.
My window is 0 ≤ x ≤ 250 and 0 ≤ y ≤ 61000
25. Behavior Science: Smoking and Education According to a study, the probability
that a smoker will quit smoking increases with the smoker’s educational level. The
probability (expressed as a percent) that a smoker with x years of education will quit
Is approximately y = 0.831x 2 18.1x + 137.3 for 10 ≤ x ≤ 16.
a. Graph this curve on the window [10,16] by [0,100].
b. Find the probability that a high school graduate smoker (x=12) will quit.
c. Find the probability that a college graduate smoker (x=16) will quit.