Algebra 2 Unit 5
Review #3: DO NOT USE A CALCULATOR
1. The area of a sphere is
Name:_________________________
Period:__________Date:__________
. Show that
. Explain why there is no ± in front of the
square root.
2.
3.
If you’re in a canoe on a river and not paddling, you will travel the same direction and at the same speed as the
river’s current. When you paddle with the current (downstream), the canoe’s speed is the sum of your paddling
speed and the current’s speed. When you paddle against the current (upstream), the canoe’s speed is the
difference of your paddling speed and the current’s speed. Suppose you paddle a canoe at a steady speed of 2
miles per hour. You go 4 miles downstream and then 4 miles upstream to get back to where you started. The trip
takes 4 hours.
4. Write expressions for the canoe’s downstream and upstream speeds. Let s be the speed of the current.
Downstream Speed:
Upstream Speed:
5. Divide the distance traveled in each direction by the canoe’s speed in that direction to find the time for
that part of the trip.
Downstream Time:
Upstream Time:
6. Write an equation that would represent the total time it takes for your canoe trip.
7. Using your equation from above, determine the speed of the current. Show your work to justify your
answer.
Suppose you can ride a bike at a steady speed of 15 miles per hour. You ride 26 miles into the wind and then
return 26 miles with the wind at your back and end up where you started. The trip takes you a total of 4 hours.
8. Write an expression for your speed with the wind, and for your speed against the wind:
With the wind:
Against the wind:
9. Divide the distance traveled in each direction by the bikes speed in that direction to find the time for that
part of the trip.
10. Write an equation that would represent the total time it takes for your bike trip.
11. Use your equation from above and determine the speed of the wind. Justify your answer.
12. Solve each of the problems for x. Check for extraneous solutions.
b.
a.
c.
d.
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13. Let
and
a. Graph both
on the coordinate plane below.
b.
State the domain and range of
c.
Describe the transformation of
to
d. Create a function that would transform
by compressing it by a factor of ½ , reflecting it
over the x axis, horizontally translating it 3 units left, and vertically translating it 2 units up.
14. Let
and
a. Fill out the table of values below for
-2
-1
b. Graph both
and
0
1
2
on the coordinate axes below.
c. Find the asymptotes indicated
horizontal asymptote of
_______________
vertical asymptote of
horizontal asymptote of
vertical asymptote of
:_________________
:_______________
:_________________
d. Complete the following statements:
e. Create a function
and 5 units up.
that transforms the parent function
by shifting it 3 units to the left
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