PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
1. Fifteen years after a study, the population of Stamford, CT was 843,576. Twenty years
after the study, the population was 956,482. Population is growing exponentially with
time.
a) Write the particular equation. Remember to use the “store” button on your calculator.
b) What was the population 17 years after the study?
c) How many years after the study will the population reach 1,500,000?
2. Write the equation of each function in the graph below.
a.
b.
c.
d.
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
3. Solve the following:
1
log 4 ( x)  2 log 4 4  log 4 16
2
4. Solve the following:
ln( 2 x  1) 3  6
5. A rocket is launched into the air and at the following times: 15, 45, 70, 85 seconds,
reaches the corresponding heights: 22000, 44200, 40700, 29000 feet.
a) Determine the quadratic function which best describes the path of this rocket.
b) What is the rocket’s height at 10 seconds?
c) At what two times will this rocket reach a height of 15000 feet?
d) When will the rocket return to the ground?
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
6. Evaluate the following limits.
a. lim
x 7
x 2 3
x7
3  x2
x 0
x2
b. lim
x2
x  3 x  2 x  8
c. lim
2
x2
x 2 x 4  16
d. lim
e.
x2  9
x 2 x  3
lim
7. Use the graph below to evaluate the following limits.
lim f  x 
b. lim f  x 
c. lim f  x 
d. lim f  x 
e. lim f  x 
f. lim f  x 
g. g  2
h. lim f  x 
a.
x0
x2
x0
x2
x4
x0
x2
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
8. Given (-9, -4), (-3, 2) and (3, -4), find the standard equation of the circle that passes
through these three points. Then state the center and radius of the circle.
9. Write the standard and general equation of a circle that has a diameter with endpoints of
(4, 8) and (-2, 0)
For numbers 10 and 11, find all vertical asymptotes, horizontal asymptotes, x intercepts, y
intercepts and any points of discontinuity that exist. Then, draw a sketch of the function.
x 2  4x  3
10. f ( x)  2
x  x6
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
2
x  3 x  10
11. f ( x) 
2
12. For number 7, find all vertical asymptotes, horizontal asymptotes, x intercepts, y
intercepts and any points of discontinuity that exist. DO NOT DRAW A SKETCH!
f ( x) 
3x 2  3x
x2  x
13. Simplify.
a)
7 3
x
4
3
320 x 5 
2
 27 x 9 y 3  3
b)  3 6 
 8x z 
5 2
x
2
3
40x 8  2 45x 7
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
14. Find the equation of a parabola with a horizontal directrix that passes through the points
(5, 3), (-3, 51) and (0, 18). Then rewrite the equation into standard form.
15. Write the general and standard equation of a parabola that has a vertex at (-1, 2), passes
through (3, 6) and has a vertical directrix.
16. Find the coordinates of the focus and the vertex and the equations of the directrix and
axis of symmetry for the parabola with the equation below. Then determine the width of
the parabola through the focus and graph the parabola.
a.
( x  3) 2  8( y  4)
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
b. ( y  12) 2  20( x  9)
17. In 1920, the population of Redding, CT was 9,432. In 1950, the population was 13,329.
If the population continued to grow at this rate, what was the population of Redding in
1980? In 2000? In what year will/did the population reach 20,000?
PreCalculus
Final Review Packet #2
Name___________________________
Date_________________________
18. Factor Completely
x18  152 x 9  13824
x2
 4 x  5 
19. Solve for x using logarithms. 3
20. Solve for x.
log 9 5 x  log 9 6  log 9 x  2