25
Section 1.2 1. Yes it is a function. It passes the vertical line test.
Section 1.2
1.
Yes it is a function. It passes the vertical line test.
No it is not a function. It fails the vertical line test.
2.
Yes it is a function. It passes the vertical line test.
3.
4-7 a.Evaluate the given expressionb.Find the domain of the functionc.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.
h(z) 1
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. , find
h(x) x1/ 4
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)
From calculator.
OR use your calculator.
8-9 Graph each function.
8.
f (x) 3x 2
9.
f (x) 2x 2 4x 16
10a.Graph the function in an appropriate window. (answers may vary)b.Find the vertex.
f (x) x 2 40x 500
a.
b. Using a calculator and minimum V (- 20, 100).
My window is - 60 ≤ x ≤ 10 and -100 ≤ y ≤ 1000
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.
4x 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.
4x 2 24x 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 footplus 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.
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
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 . Find the size of the culture after a. 2 days b. 10 days
N(t) 20050t 2
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:
a.Find the company’s break-even points.b.Find the number of devices that will maximize profit, and the maximum profit.
c(x) 180x 16000
R(x) 2x 2 660x
a. To find the break-even points graph 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 quitIs 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.
