Question

Directions: What the type of translation of f(x) = x

Answer 1

1. Horizontal translation of 2 units to the right.

2. Vertical shift up 1 unit.

3. vertical shift down 3 units:

4. horizontal translation 3 units to the left

1) We can see that these functions are actually transformed versions of the parent function f(x)=|x|

2) So examining each one we can state the following:

1.

$g(x)=|x-2|$

Note that this function is a horizontal translation of 2 units to the right.

2. The following function, on the other hand, with the +1 outside the absolute value bars is a vertical shift or vertical translation up 1 unit.

$g(x)=|x|+1$

3. Similarly, we can see that this one presents a vertical shift down 3 units:

$g(x)=|x|-3$

4. Finally, in this last one, we have a horizontal translation 3 units to the left:

$g(x)=|x+3|$

Thus the answer is:

1. Horizontal translation of 2 units to the right.

2. Vertical shift up 1 unit.

3. vertical shift down 3 units:

4. horizontal translation 3 units to the left