MATH 106 West Valley College Algebra Worksheet

Math 106 Test 3You may use one 3” by 5” notecard and a non-graphing calculator for the test. Carefully read all the instructions
and clearly show all your work.
1. (8 points) Simplify: √
2. (8 points) Solve:
100𝑥 3
𝑦4
√𝑥 − 8 − 4 = 1
3. (8 points) Rationalize the denominator:
√5
√2 + √3
4. (8 points) Multiply and simplify: (2 − 5𝑖)2
5. (15 points) For the function
𝑓(𝑥) = 𝑥 2 − 4𝑥 − 5
a. Identify the end behavior of the graph (shape and direction of graph on both ends). You can
simply draw the shape, and do not have to describe it in words.
b. Find the vertex of the graph of 𝑓(𝑥).
c. Find 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 of the graph of 𝑓(𝑥).
d. Find y-intercept of the graph of 𝑓(𝑥).
e. Graph 𝑓(𝑥). Clearly show the vertex and
all the intercepts.
f. Find the domain and range. Write your
answer in the interval notation.
6. (8 points) Use the properties of logarithms to expand as much as possible:
log 2 (
√𝑥 2 +1
8
)
7. (8 points) Solve the inequality and write your solution in the interval notation.
(2𝑥 − 5)2 (𝑥 + 6) ≤ 0
8. (10 points) The exponential model 𝐴 = 91.1𝑒 0.0127𝑡 describes the population of the Philippines, in
millions, 𝑡 years after 2007. (Round your answer to one decimal place.)
a. Use the model to estimate the population in the Philippines in 2015.
b. When will the population of the Philippines be 122 million?
9. (12 points) Solve:
a. 𝑙𝑜𝑔𝑥 = 2
b. 52𝑥−1 = 625
10. (8 points) Solve using the Quadratic Formula and leave your answer in the exact form:
2𝑥 2 − 𝑥 = 7
11. (7 𝑝𝑜𝑖𝑛𝑡𝑠) 𝑓(𝑥) = 2𝑥 − 5; 𝑔(𝑥) = 4𝑥 + 8. 𝐹𝑖𝑛𝑑 (𝑓 ∘ 𝑔)(𝑥)