Question

\Fill in the blanks to describe the transformations.

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

To describe the transformations of the given functions, let's analyze them one by one:

1. For the transformation **f(x) → f(x+2) + 1**:
- The term **(x + 2)** indicates a translation to the **left** by **2** unit(s) because you are adding 2 inside the function.
- The **+1** outside the function indicates a vertical translation **up** by **1** unit(s).
- So, you can fill in the blanks as:
- It is translated **2** unit(s) to the **left** and **1** unit(s) **up**.

2. For the transformation **f(x) → f(x−5) + 4**:
- The term **(x - 5)** indicates a translation to the **right** by **5** unit(s) because you are subtracting 5 inside the function.
- The **+4** outside the function indicates a vertical translation **up** by **4** unit(s).
- So, you can fill in the blanks as:
- It is translated **5** unit(s) to the **right** and **4** unit(s) **up**.

3. For the transformation **f(x) → f(x−3) - 6**:
- The term **(x - 3)** indicates a translation to the **right** by **3** unit(s) as you are subtracting 3 inside the function.
- The **-6** outside the function indicates a vertical translation **down** by **6** unit(s).
- So, you can fill in the blanks as:
- It is translated **3** unit(s) to the **right** and **6** unit(s) **down**.

In summary, here are the completed transformations:

1. It is translated **2** unit(s) to the **left** and **1** unit(s) **up**.
2. It is translated **5** unit(s) to the **right** and **4** unit(s) **up**.
3. It is translated **3** unit(s) to the **right** and **6** unit(s) **down**.