Final ExamMath 106, West Valley College, Fall 2021

You may use one 3β by 5β notecard and a non-graphing calculator for the test. Carefully read all the

instructions and clearly show all your work. Box your final answers. Good Luck!!!βΊ

1. (7 points each) Simplify completely:

a.

b.

1

π₯ 2 +8π₯+15

1

π₯β1

+

Γ·

2

π₯β5

3

π₯+5

6π₯ β5 π¦

2

c. ( 2 β4 )

2π₯ π¦

d. 7β9π₯ 9 + π₯ 4 β25π₯

2. (7 points) Use the properties of logarithms to expand as much as possible:

log 3 (

β(π₯+1)

27

)

3. (15 points) A ball is thrown straight up from a height of 3 feet. The ballβs height in feet above the

ground, t seconds after it is thrown, can be modeled by the function

β(π‘) = βπ‘ 2 + 2π‘ + 3

a. Write and solve a quadractic equation to find when the ball will hit the ground. Round your

answer to one decimal.

b. When will the ball reach the maximum height?

c. What will be the maximum height of the ball?

4. (7 points each) Multiply and Simplify:

a.

(2 β 5β3)(2 + 5β3)

b. (7 β 4π)2

5. (10 points) Find the vertex and intercepts of the given quadratic function. Then use it to sketch

the graph of the quadratic function. Use the

graph to identify the range of the quadratic

function.

π(π₯) = (π₯ β 1)2 β 9

a. Vertex:

b. π₯ β πππ‘ππππππ‘(π ):

c. π¦ β πππ‘ππππππ‘(π ):

d. Domain:

e. Range:

6. (6 points) Find the equation of the line passing through the point (β6, 5) and parallel to the line

1

whose equation is π¦ = π₯ + 5.

3

7. (6 points) Solve the linear inequality:

3(π₯ + 5) β 5 < 6π₯ β 3(π₯ β 3)
8. (10 points) The formula π΄ = 36.1π 0.0126π‘ models the population of California, A, in millions, t years
after 2005.
a. Use the model to estimate the population in the California in 2012.
b. When will the population reach 40 million?
9. (7 points) Find the restrictions and solve:
3π₯
4
+
=3
π₯+1 π₯β2
10. (6 points) Solve the given system of equations (write your final answer as a co-ordinate):
2π₯ + 3π¦ = 10
3π₯ + π¦ = 1
11. (8 points each) Solve:
a.
ππππ₯ = 4
b. 72π₯β1 = 49
12. (6 points each) Find the indicated function values for the function π(π₯) = 4π₯ β 2.
a. π(β5)
b. π(π + β)
13. (10 points) Find the π₯ β πππ
π¦ βintercepts:
3π₯ β 4π¦ = 36.
14. (7 points) Find the domain and write it in the interval notation: π(π₯) = β2π₯ β 10
15. (8 points) Using the slope and the π¦ β
πππ‘ππππππ‘ to graph:
4
π¦ =β π₯β1
5
16. (8 points) Solve using the Quadratic Formula and leave your answer in the exact form:
2π₯ 2 β π₯ = 5
17. (7 points) Let π(π₯) = β2π₯ β 5 and π(π₯) = π₯ 2 + 3π₯. Find (π β π)(π₯)
18. (7 points each) Factor completely:
a. 4π₯ 4 π¦ 5 + 28π₯ 3 π¦ 3 + 16π₯ 2 π¦ 9
b. π₯ 3 β 15π₯ 2 β π₯ + 15
c. 4π₯ 2 β 8π₯ β 5
19. (10 points) Answer the questions after analyzing the graph given below. You may assume that the
graph continues at the right end.
a. Determine if π¦ is a function of π₯. You must give reason.
b. Find the domain of the function. Write your answer in interval notation.
c. Find the range of the function. Write your answer in interval notation.
YAY, you are DONE!!!! Wait, did you check your work?
Happy Holidays!!!

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