state the various transformations applied to the base function ƒ(x) = |x| to obtain a graph of the function g(x) = 3[|x − 1| + 2].
horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3.
horizontal shift of 3 units to the right, a vertical shift downward of 2 units, and a vertical stretch by a factor of 3.
horizontal shift of 3 units to the left, a vertical shift upward of 2 units, and a vertical stretch by a factor of 3.
horizontal shift of 1 unit to the left, a vertical shift downward of 6 units, and a vertical stretch by a factor of 3.

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..

Step-by-step explanation:

Given function is:

3[|x-1|+2]

Can also be written as:

3|x-1|+6

As we can see that the -1 is grouped with x which means it is a horizontal shift of 1 unit to the right.

Now, 6 is added to the function and it is not grouped with x which means that there is a vertical shift of 6 units upward.

Lastly, 3 is multiplied with the term containing x which means that there is a vertical stretch of 3 units.

Hence, the correct option is:

Horizontal shift of 1 unit to the right, a vertical shift upward of 6 units, and a vertical stretch by a factor of 3 ..