Fill in the blanks to describe the transformations.

Question

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.