Download ALGEBRA 2

Algebra II – Pre AP
Review 7.1-7.4
Name: __________________________________
NO CALCULATOR
Graph the following, state the domain and range. Draw and label any asymptotes. Plot 3 points.
1.
3
f ( x)  2  
2
x
2.
y  2 x 1  3
Domain:
Domain:
Range:
Range:
3.
y  3 x
4.
f ( x)  4(.5) x 2  1
Domain:
Domain:
Range:
Range:
1. f ( x)  log 1 x  2
2. f ( x)  log5 ( x  2)  1
y
y
3
2
2
2
Domain
2
x
O
Range
Domain
Asymptote_______________
Range
Asymptote_______________
y
y
1
4. f ( x)  ln x  1
2
3. f ( x)   log 2 ( x  3)
2
5
2
2
O
Domain
Range
Asymptote_______________
x
O
2
x
O
Domain
Range
Asymptote_______________
x
Graph the following state the domain range and asymptote.
y
12. y = ex – 1 + 1
y
13. y = 3e-x
2
2
2
2
x
O
O
Domain_____________
Domain_____________
Range______________
Range______________
Asymptote_______________
Asymptote________________
x
For #5-6, identify the horizontal asymptote of the following equations.
5.
y  24
x2
1
6.
_______________
1
y  2 
 3
x2
5
_______________
For #6-7, write the new equation.
x
6.
1
If the parent function, y    is shifted 2 units to the right and 3 units down, what is its new equation?
4
y = _____________________
7.
If the parent function, y  4x is reflected over the x-axis and shifted to the left 6 units, what is its new
equation?
y = _____________________
8.
Describe the transformation that occurred from y  3 x  2  6 to y  3 x4  2 .
______________________________________________________________
Simplify the expressions:
 5e 
3x 3
9. 3e4 ● e3
10.
__________________
___________________
e4 x
11. 5e
__________________
Evaluate the following expressions.
1
3
5. log 8 1
6. log 3
7. log 9 81
8. log 4 4 2 3
7. log 5 5  log 5 25
8. log 0.001
Expand the following expressions.
9.
log x 2 yz
10. log 7
1
yz
3
11. ln 5x 3
________________________
Condense the following expressions.
12. 2 ln x  ln 3  ln 6
13. log 3 4  log 3 2  log 3 2
14. log x  (log 4  3log y)
________________________
Solve each equation.
1.
1
3x  27
2.
1
4 x  16
3.
6 x9  363 x
4.
5.
8x2  16
6.
6 x  50
7.
32 x1  15
8. 25 x
9.
log27 x = 23
10.
log2 64 = 5x + 1
5x2  254 x
 
11.
x5
log3 729 = 2x
2
 32 x 10
12.
log9 (x2  8x) = log9 9
13.
log2 x + log2 8 = log2 (x + 14)
14.
log4 x + log4 (x  6) = log4 (-8)
15.
log9 (x + 1)  log9 (x + 5) = log9 3  log9 7
16.
2 log3 x  log3 (x + 4) = 2
17.
log5 (x2 + 7) = 23 log5 64
18. Carl plans to invest $4500 at 8.25% interest. How long will it take for his money to triple if…
a. the interest is compounded quarterly?
b. the interest is compounded monthly?
19. A certain strain of bacteria grows from 20 to 326 in 2 hours.
a. How many bacteria will there be after 7 hours?
b. How long will it take for the bacteria to triple?
c. For the number of bacteria to reach 50,000?
20. Nancy secures a loan for a new car of $40,000 at 7.6% annual interest.
a. What will her monthly payments be if she takes a 5 year loan?
b. What will her monthly payments be if she takes a 4 year loan?
c. How much money will she save if she takes a 4 year loan as opposed to a 5 year loan?
d. An independent bank offers her a loan for this car at 6.8% annual interest for 8 years. Does it
make financial sense for her to take this loan instead?
1.
The value of a car can be modeled by y  a(0.75)t where y is the value of the car, a is the initial cost of the
car and t is the time (in years) since the car was manufactured. The initial cost of the car was $25,000.
_______________a. Does the model represent exponential growth or exponential decay?
_______________b. What is the value after 9 years?
2.
The growth of bacteria in a lab is modeled by y  2000(1.5)t where y is the number of bacteria and t is the
time in hours.
_______________a. What is the initial number of bacteria?
_______________b. Does the model represent exponential growth or exponential decay?
_______________c. What is the number of bacteria after 6 and half hours?
3.
You deposit $4000 in an account that pays 2.5% annual interest compounded continuously.
_______________a. What is the value of the account at the end of 5 years?
4.
On your birthday, you receive an iPad worth $400. The value of the iPad decreases by 20% each year.
_______________a. What is the initial amount?
_______________b. What is the percent of decrease?
_______________c. What is the decay factor?
_______________d. Find the value of the iPad at the end of 4 years.
5. You deposit $3500 in an account that earns 2.5% annual interest. Find the balance after one year if the interest
is compounded with the given frequency.
a. quarterly _______________________
b. monthly ________________________
6. Carl plans to invest $4500 at 8.25% interest. How long will it take for his money to triple if…
a. the interest is compounded quarterly?
b. the interest is compounded monthly?
7. A certain strain of bacteria grows from 20 to 326 in 2 hours.
a. How many bacteria will there be after 7 hours?
b. How long will it take for the bacteria to triple?
c. For the number of bacteria to reach 50,000?
8. Nancy secures a loan for a new car of $40,000 at 7.6% annual interest.
a. What will her monthly payments be if she takes a 5 year loan?
b. What will her monthly payments be if she takes a 4 year loan?
c. How much money will she save if she takes a 4 year loan as opposed to a 5 year loan?
d. An independent bank offers her a loan for this car at 6.8% annual interest for 8 years. Does it
make financial sense for her to take this loan instead?