Algebra Questions

1.

What does this mathematical symbol ∞ represent?

Zero

 

Infinity

 

Pi

 

Undefined

 

2.

A rational expression can be written as a ratio of two polynomial expressions.

True

False

 

3.

Asymptotes are invisible lines which a graphed function will approach very closely but not touch.

True

False

 

4.

Find the domain of the function 

 

Domain: all real numbers x except x=6

 

Domain: all real numbers x except x=8

 

Domain: all real numbers x

 

Domain: all real numbers x except x = -6

 

5.

Find the domain of the function 

 

Domain: all real numbers x except x = 7

 

Domain: all real numbers x except x = ±49

 

Domain: all real numbers x except x = -7

 

Domain: all real numbers x except x = ±7

 

6.

Find the domain of 

 

all real numbers except x = -9

 

all real numbers except x = 81

 

all real numbers except x = 9

 

all real numbers except x = 9 and x = -9

 

7.

Find the domain of the function and identify any vertical and horizontal asymptotes.

Domain: all real numbers x except x = 2

Vertical asymptote: x = 2

Horizontal asymptote: y = -1

 

Domain: all real numbers x except x = 0

Vertical asymptote: x = 0

Horizontal asymptote: y = -1

 

Domain: all real numbers x except x = 2

Vertical asymptote: x = 0

Horizontal asympotote: y = -2

 

Domain: all real numbers x except x = -2

Vertical asympotote: x = 0

Horizontal asympotote: y = 2

 

8.

Select the correct graph of the function. Choose from among the graphs listed below: 1st, 2nd, 3rd, or 4th.

9.

The cost C (in millions of dollars) of removing p% of the industrial and municipal pollutants discharged into a river is given by

According to this model, it is possible to remove 100% of the pollutants.

True

False

 

10.

Based on your answer to problem 9, explain why you chose your answer (whether it is possible or not to remove 100% of the pollutants).

 

11.

In the following formula, S(x) is the minimum number of hours of studying required to attain a class score of x. How many hours of study are needed to score 85? Round your answer to the nearest whole number.

 

12.

The concentration C (in mg/dl), of a certain antibiotic in a patient’s bloodstream is given by C(t)=50 t /(t^2 + 25) where t is the time (in hours) after taking the antibiotic. What is the concentration 5 hours after taking the antibiotic?

 

13.

In order to join a gym, you pay a $200 annual fee, then $10 for each exercise class you attend. Indicate which equation below would allow you to determine the average cost per class if you go to x amount of classes: 1st, 2nd, 3rd, or 4th.

14.

Which of the following can a graph NEVER cross:

 

Vertical asymptote

 

Horizontal asymptote

 

Slant asymptote

 

All of the above

 

15.

Select the graph of the rational function. Choose from among the graphs below: 1st, 2nd, 3rd, or 4th.

16.

One pipe can fill a pool in 1.5 hours. A second pipe can fill up the pool in 2 hours. Which of the equations below would determine how long it would take to fill the pool when both pipes are used? Select the correct equation:1st, 2nd, 3rd, or 4th.

17.

Using the equation you wrote in the last problem, how long would it take to fill the pool if both pipes are open at the same time? Write your answer in fraction form.

 

18.

Evaluate the function at the indicated value of x. Round your result to three decimal places.

 

Function: f(x) = 0.5^x Value: x = 1.7

 

-0.308

 

1.7

 

0.308

 

0.5

 

19.

Solve for x. 3x = 81

 

7

 

3

 

4

 

-3

 

20.

Logarithms are the inverse of exponentials.

True

False

 

21.

The Logarithm Quotient Rule states:

logb(x / y) = logb(x) + logb(y)

 

logb(x / y) = logb(x) – logb(y)

 

logb(x y) = y ∙ logb(x)

 

logb(c) = 1 / logc(b)

 

22.

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. Assume all variables are positive.

log3 9x

 

 

log3 9 x log3 x

 

log3 9 + log3 x

 

log3-9 log3

 

none of these

 

23.

Select the graph of the function. Indicate which graph is correct: 1st, 2nd, 3rd, or 4th

f(x) = 5x-1

 

24.

Evaluate the function at the indicated value of x. Round your result to three decimal places.

f(x) = 500e(.05)x  Value: x=2

 

25.

The exponential equation y=bx is equivalent to the logarithmic equation x=logby

True

False

 

26.

Use the One-to-One property to solve the equation for x.

e(3x+5) = e6

 

27.

Write the logarithmic equation in exponential form.

log8 64 = 2

 

28.

Write the exponential equation in logarithmic form.

43 = 64

 

29.

The given x-value is a solution (or an approximate solution) of the equation.

42x-7 = 16

x = 5

 

true

false

 

30.

Find the magnitude R of each earthquake of intensity I (let I0=1). (Hint: R=log (I/I0)

I = 19000

 

3.28

 

5.28

 

4.28

 

2.38

 

31.

pH is a measure of the hydrogen ion concentration of a solution. It is defined as the negative logarithm of the hydrogen ion concentration. The equation is:

pH = – log [H+]

If an acid has an H+ concentration of 10-4, what’s the pH?

 

32.

A general formula for exponential Growth can be given by:

A = P ekt

Using another reliable source, research what values, P, A, k and t represent and write your answer. (Hint: What do each of the variables stand for?)

 

33.

Continuously compounded interest means your principal is earning interest and you keep earning interest on the interest earned. Research the formula for Continuously Compounded Interest and write it below.

 

34.

$2500 is invested in an account at interest rate r, compounded continuously. Find the time required for the amount to double. (Approximate the result to two decimal places.)

r = 0.0570

 

35.

Write Eulers Number (e) to three decimal places.

 

36.

Exponential functions often involve the rate of increase or decrease of something such as a population, for example. If there is a population increase, it is a _______ function and when there is a decrease, it is a ________ function.

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