Question

Fill in the blanks to describe the transformations.

Describe the translations stating the horizontal first and the vertical shift second

f(x) → f(x+2)+1
: It is translated
unit(s) to the
and
unit(s)
f(x) → f(x−5)+4
: It is translated
unit(s) to the
and
unit(s)
f(x) → f(x−3)−6
: It is translated
unit(s) to the
and
unit(s)

Answer 1

Let's analyze each transformation step by step:

1. For \( f(x) → f(x+2) + 1 \):
- The "+2" indicates a horizontal shift to the **left** by 2 units (since we have \(x + 2\)).
- The "+1" indicates a vertical shift **up** by 1 unit.
- Thus, it is translated **2** unit(s) to the **left** and **1** unit(s) **up**.

2. For \( f(x) → f(x−5) + 4 \):
- The "-5" indicates a horizontal shift to the **right** by 5 units (since we have \(x - 5\)).
- The "+4" indicates a vertical shift **up** by 4 units.
- Thus, it is translated **5** unit(s) to the **right** and **4** unit(s) **up**.

3. For \( f(x) → f(x−3) − 6 \):
- The "-3" indicates a horizontal shift to the **right** by 3 units (since we have \(x - 3\)).
- The "-6" indicates a vertical shift **down** by 6 units.
- Thus, it is translated **3** unit(s) to the **right** and **6** unit(s) **down**.

Here's the summarized information:

1. \( f(x) → f(x+2) + 1 \): It is translated **2** unit(s) to the **left** and **1** unit(s) **up**.
2. \( f(x) → f(x−5) + 4 \): It is translated **5** unit(s) to the **right** and **4** unit(s) **up**.
3. \( f(x) → f(x−3) - 6 \): It is translated **3** unit(s) to the **right** and **6** unit(s) **down**.