Algebra Answers

A store is having a special sale on designer soaps. For every three bars of soap purchased, one is given for free. The bars of soap cost $2 each, and there is a limit of 8 bars of soap per customer (including free ones).

a. Write a piecewise defined function C (b) that gives the total cost C for b bars of soap.

b. Write the domain for this function in terms of the context.

Q. Draw the graph of following functions on graph paper.
(i) y=x
(ii) y=x+1
(iii)y=x-1
(iv)y=x+2
(v)y=2x
(vi)y=3x+5
(vii)y=-x+1
(viii)y=-x+2
(ix)y=-x
(x)y=-x-1

1: Which of the following are true statements about the expression 12^5
Check all that apply.

: 12 is the exponent and tells us how many times we should multiply 5 by itself.
: 12 is the base
: 5 is the base
: 5 is the exponent and tells us how many times we should multiply 12 by itself.


2: If n√a = r , then which of the following are true statements?
Check all that apply.

a^r = n
a^1/n = r
n^1/r = a
r^n = a

8: Which function has a removable discontinuity?
A: f(x) = 5x/1 – x^2
B: g(x) = 2x – 1/x
C: h(x) = x^2 – x – 2/x + 1
D: p(x) = x/x^2 – x – 2


9: What is the equation of the oblique asymptote?

h(x) = x^2 – 3x – 4/x + 2

A: y = x + 4
B: y = x – 5
C: y = x
D: y = x – 4


10: Which function has the following characteristics?
A vertical asymptote as x = 3
A horizontal asymptote at y = -1/2

A: y = -x/ 2x^2 – x – 12
B: y = -x^2/ 2x^2 – 2x – 12
C: y = x/ 2x^2 – x – 3
D: y = -1/ 2x^2 – 2x – 6

4: What is the domain for the following function?

Y = 4/x^2 + 1

A: (x ≠ 3)
B: (x ≠ 0)
C: (all real numbers)
D: (x ≠ - 3)

5: What is the range for the following function?

1
y = ------ + 2
x + 3

A: {y: y Σ R, y ≠ 2}
B: {y: y Σ R, y ≠ 3}
C: {y: y Σ R)
D: {y: y Σ R, y ≠ - 2}
If you do not recognize the Σ in this equation that is because it is being used in replace of a similar looking shape, likewise though I doubt it has a big influence on the outcome of the answer.

7: Which function does not have a vertical asymptote.

A: y = 5x – 1/x
B: y = x/1 + x^2
C: y = 5x/1 – x^2
D: y = 5x/x + x^2

1: Which is a rational function?

A: y = x-5/x
B: y = 5
C: y = x^2 – 3x + 5
D: y = √x-3

2: y = 2x^2/ 3x^2 -16

what is the horizontal asymptote for the above function?
Y= ____________

3: y = 1/x – 5

What is the vertical asymptote for the above function?
X= _____________

The college bookstore sells CD for $15.50 and study guides for $21.50. One day, the number of study guides sold was four more than three times the number of CDs. If the total sale were $566, how many of each did the bookstore sell?

19: Air pressure may be represented as a function of height (in meters) above the surface of the earth, as shown below.

P(h) = Po ∙ e^-0.00012h

In this function, Po is the air pressure at the surface of the earth, and h is the height above the surface of the earth, measured in meters. At what height will the air pressure equal 50% of the air pressure at the surface of the Earth?

A: 0.59 m
B: 5776.2 m
C: 2148.9 m
D: 4166.7 m



20: If you were to place $5,000 in savings account that pays 6% interest compounded continuously, how much money will you have after 4 years? Assume you make no other deposits or withdraws.

A: $5,024
B: $11,821.07
C: $6,356.25
D: $6,312.38

16: Simplify the expression shown below:

In(e^3 x^4)

A: 3x^4
B: 12e
C: 7In(x)
D: 3 + 4In(x)


17: Solve the equation below x:

100 = 25e^3x

A: x = In4/3

B: x = In100/3 ∙ In25

C: x = 4/e^3

D: x = In4 – 3


18: The population (in millions) of a certain country can be approximated by the function P(x) = 50(1.03)^x , where x is the number of years since 2000. In which year will the population reach 100 million?

A: 2023
B: 2066
C: 2002
D: 2132

13: Let logbA = 3; logbC = 2; logbD = 5

D^2
What is the value of logb ---------
C^3 A

A: 19
B: 1
C: 0.549
D: 4.44

P M
14: Let log ---- = 6 and log ---- = 8. What is the relationship between P and M?
N N

A: P = 100M
B: M = 100P
C: M = .001P
D: M = 2P


15: Solve the equation below for x:

log2x + log(x – 1) = log6x

A: There are no solutions.
B: x = -1/3
C: x = 4
D: x = 0, 4