Module 3  Answers 
Lesson 1 
Answer 1 
3.1.1
The graph of is a vertical stretch of by a factor of 3. The graph of is a vertical shrink (or compression) of the graph of by a factor of 1/2. 
Answer 2 
3.1.2
is a reflection across the xaxis of . 
Lesson 2 
Answer 1 
3.2.1
is a vertical shift of up 5. is a vertical shift of down 4. 
Answer 2 
3.2.2 produces a horizontal shift of to the right 3 units. 
Answer 3 
3.2.3
The graph of
is the graph of
:

Lesson 3 
Answer 1 
3.3.1
If the transformed graph will be a vertical shrink. If the transformed graph will be a vertical stretch. If a < 0, the transformed graph will be a reflection across the xaxis. 
Answer 2 
3.3.2 According to the table the investment will have grown to approximately $1418.52 in six years. 
Answer 3 
3.3.3
The investment will double in approximately 12 years, which agrees with the solution found from the table of values. 
Answer 4 
3.3.4
About 3.15 grams remain after 50 days. 
Answer 5 
3.3.5
There will be 1 gram remaining after about 100 days. 
Answer 6 
3.3.6 Y_{2} = log(2x) appears to be a vertical shift of Y_{1} = log(x). 
Answer 7 
3.3.7 The third graph suggests that the difference in the first two functions is a constant. In other words: Y_{2} – Y_{1} = C so Y_{2} = Y_{1} + C. This last equation supports the conjecture that Y_{2} is a vertical shift of Y_{1}. 
Answer 8 
3.3.8 For positive values of a and x, log(ax) = log(x) + log(a). 
Lesson 4 
Answer 1 
3.4.1
The xvalue that yields an output close to 30 is x = 40. So the transformed regression equation predicts that the water will cool to approximately 30°C in a bit less than 40 minutes, which corresponds well with the data. 
Self Test 
Answer 1 
Any ordering of these 4 transformations will result in the correct graph as long as the vertical stretch and reflection are done before the vertical shift. Reflect across the xaxisVertical stretch by factor of 2 Shift left 1 Shift down 3

Answer 2 
The investment will double in about 10.2 years 
Answer 3 
x 222.4 
Answer 4 
Y_{2} is a vertical shift of Y_{1} downward and the shift is equal to log(2). 
Answer 5 
y = 64(0.93)^{x} + 23 
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