Download Calculus Chapter 2 Review

Chapter 2 TEST Review
𝑟 𝑛𝑡
𝐴 = 𝐴0 𝑒 𝑘𝑡


*** Do NOT write on worksheet. ***
𝐴 = 𝑃 (1 + 𝑛)
𝐴 = 𝑃𝑒 𝑟𝑡
𝑥 −5𝑥+6
2𝑥
Find the domain of each function:
3𝑥
1. 𝑦 =
2. 𝑦 = √3𝑥 + 9

Find the domain and range of each parent and child:
1. 𝑦 = ln 𝑥 ; 𝑦 = ln(𝑥 + 2) − 3
2. 𝑦 = 3𝑥 ; 𝑦 = −3𝑥 +4
Solve for all values of x. Round x to 2 decimal places.
1. 8000 = 4000𝑒 (𝑥+4)
2. 52𝑥−3 = 7.08
3. ln(2𝑥 − 2) − ln(𝑥 − 1) = ln 𝑥
4. 𝑙𝑜𝑔2 (𝑥 + 4) + 𝑙𝑜𝑔2 (𝑥 − 3) = 3
Polynomials and graphs:
1. What is the least degree of the polynomial for Graph 1?
2. State the end behavior of Graph 1.
3. Write the equation for the lowest degree polynomial of Graph 2.

0
(𝐼0 = 10−16 𝑊/𝑐𝑚2 )
Graphing Calculator Problems
1. Solve by graphing: 1.9𝑥 2 − 1.5𝑥 − 5.6 < 0 Write your answer using interval notation and
numbers rounded to 2 decimal places.
2. The marketing research department for a company that makes and sells computer chips
established the price-demand function 𝑝(𝑥) = 75 − 3𝑥 where p(x) is the wholesale price in
dollars at which x million chips can be sold and 1 ≤ 𝑥 ≤ 20. R(x) is in millions of dollars.
A. Write the revenue function R(x).
B. Sketch a graph of R(x) where 1 ≤ 𝑥 ≤ 20, 0 ≤ 𝑦 ≤ 500
C. How many millions of computer chips will produce the maximum revenue?
D. What is the maximum revenue?
E. What is the wholesale price per chip that produces the maximum revenue?
3. Pg 117: #89
4. How long will it take an account to double in value if it is compounded continuously at a rate of
6.75%? Round to one decimal place.
5. If $5000 is put into an account that is compounded every 4 months at a rate of 7.05%, how much
will be in the account after 10 years?
6. If after 100 years, 25 mg of a piece of gum remains how much gum was there to start? (use the
decay constant -0.000124) Round your answer to 1 decimal place.
For each function, state: domain, locations of holes, equations of asymptotes, x-intercepts, and yintercepts.
𝑥−2
9−4𝑥
1. 𝑦 = 2
2. 𝑦 =


𝐼
𝑁 = 10 ∙ 𝑙𝑜𝑔 𝐼
√𝑥−5
Graph 1
Graph 2
Solutions
Graphing Calculator Problems
1. (-1.37, 2.16)
2. Application:
a. R(x) = xp(x) = 75𝑥 − 3𝑥 2
b. See graph to the right
c. 12.5 million computer chips will produce a maximum revenue.
d. The maximum revenue is 468.75 million dollars.
e. The wholesale price of 12.5 million chips is p(12.5) = $37.50 per chip.
3. See answer in back of textbook.
4. It will take 10.3 years for the money to double.
5. After 10 years, there will be $10,037.03 in the account.
6. There was 25.3 mg of gum to start.
For each function, state: domain, locations of holes, equations of asymptotes, x-intercepts, and y-intercepts.
1. Domain: (−∞, 2) ∪ (2,3) ∪ (3, ∞)
Hole: (2, -1)
VA: x = 3
HA: y = 0
X-int: none
y-int: -1/3
HA: y = -2
x-int: 2.25
y-int: none
2. Domain: (−∞, 0) ∪ (0, ∞)
Hole: none
VA: x = 0
Find the domain of each function:
1. (5, ∞)
2. (−3, ∞)
Find the domain and range of each parent and child:
1. (Parent) D: (0, ∞) R: (−∞, ∞)
2. (Parent) D: (−∞, ∞) R: (0, ∞)
(Child) D: (−2, ∞) R: (−∞, ∞)
(Child) D: (−∞, ∞) R: (−∞, 4)
Solve for all values of x. Round x to 2 decimal places.
1.
2.
3.
4.
x  -3.31
x  2.11
x=2
x=4
Polynomials and graphs:
1. Least degree is 5
2. X  +, y  - X  -, y  
3. p(x) = x(x-1)(x+1) = 𝑥 3 − 𝑥