\Fill in the blanks to describe the transformations.

Question

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.