Module 3 - Functions and Transformations

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 x-axis 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

Reflected about the x-axis.
Vertically compressed by a factor of 1/3.
Shifted left 5.
Shifted down 1.

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 x-axis.

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 Y₂ = log(2x) appears to be a vertical shift of Y₁ = 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: Y₂ – Y₁ = C so Y₂ = Y₁ + C. This last equation supports the conjecture that Y₂ is a vertical shift of Y₁.

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

Make sure that the transformed regression equation is stored in Y₂.
In the TBLSET editor, set TblStart = 0 and Tbl = 10.

Display the table by pressing [TABLE].

The x-value 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 x-axis
Vertical stretch by factor of 2
Shift left 1
Shift down 3

Answer 2

The investment will double in about 10.2 years

Answer 3

222.4

Answer 4

Y₂ is a vertical shift of Y₁ downward and the shift is equal to log(2).

Answer 5

y = 64(0.93)^x + 23