Question

Help pleaseeeeee!

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.

Answer 1

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

Explanation:

First we re write the equation by multiplying the number
`3` in this way we will see much better the solution

`g(x)=3[|x-1|+2]=3|x-1|+6`

we will start from the inside to the outside

`|x-1|` this
`-1`is grouped with the x and this means there is a horizontal shift of
`1` unit to the right (because of the sign)

`3|x-1|` this
`3` is multiplying the x which means the function will be stretching by a factor of
`3` (
`g(x)` will be
`3` times bigger)

`3|x-1|+6` this
`6` is not goruped with x and moves the entire function 6 units upwards.

We can see it more clearly in the graph attached.

Answer 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 ..

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 ..