Chapter 6 review posted online
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1. For each sequence defined recursively, write the first 5 terms. Then use the terms to write an explicit equation.
𝑎1 = 7
𝑎𝑛 = 3𝑎𝑛−1
2. If 𝑓(𝑥)
𝑎1 = −8
𝑎𝑛 = 𝑎𝑛−1 + 4
1
= 𝑥+2 + 2 find each of the following values.
𝑎. 𝑓(−2)
𝑏. 𝑓(−3)
c. Find x if 𝑓(𝑥) = 3
3. The temperature is 43 degree Fahrenheit. Your friend form France is more comfortable with Celsius
9
degrees. What is the degree in Celsius? 𝐹 = 5 𝐶 + 32
4. For Einstein’s theory of relativity, energy equals mass times speed of light squared. Solve for c?
𝐸 = 𝑚𝑐 2
5. Solve for x:
2y = 4(3x – 2) + 5x - 4y
6. Given the model below and the y: 2.5x + 55,find the residual when you sleep 7 hours.
Hours of Sleep
Grades
2
60
1
50
5
68
7
70
8
90
10
95
a. Using the above model and table, interpret what it means if the residual is negative.
b. Plot the above data, and draw the upper and lower bound. Write the equation for the upper and lower bound of the
model.
7. The table below gives the height and shoe sizes of six randomly selected men.
Height (in)
67
70
73.5
75
78
66
Shoe size
8.5
9.5
11
12
13
8
a. Scale and graph a scatter plot using the given data. Be sure to label your axes.
b. Construct a line of best fit
c. Find the equation for the line you just
constructed
d. Find the residual for a man 70 inches tall.
e. Predict the shoe size of someone who is
81 inches tall.
f.
Predict the height of someone with a 10.5 shoe size.
g. Interpret the slope in context
h. Interpret the y-intercept in context.
8. Describe the correlation illustrated by each scatter plot. Justify your reasoning.