Question

Could you do this for me?

Answer 1

This is what I think

Explanation:

Look at the coordinates of maximum in the graph `y=f(x)`
`=(0,1)`
Coordinates of maximum in the new graph `=(1,3)`

Comparing both we observe that in the new graph
`1` is added to value of `x`
`2` is added to value of `y`

Now look at the coordinates of minimum in the graph `y=f(x)`
`=(2,-1)`
Coordinates of minimum in the new graph `=(3,1)`

Comparing both we observe again that in the new graph
`1` is added to value of `x`
`2` is added to value of `y`

These points are easy to locate.

For any value added to `x`, the function is stated as
`(x-"added value")`
For any value subtracted from `x`, the function is stated as
`(x+"subtracted value")`

In case of `y`
For any value added to `y`, the function is stated as
`(y+"added value")`
For any value subtracted from `x`, the function is stated as
`(y-"subtracted value")`

Note the difference of sign in `x` and `y` respectively.
As such all points on graph `y=(x)` can be mapped on the other graph as above.

Hence option (E)

Answer 2

`E`

Explanation:

`"consider the coordinates of the stationary points"`

`"max at "(0,1)to" max at "(1,3)`

`"min at "(2,-1)to" min at "(3,1)`

`"both have been translated by "((1),(2))`

`f(xcolor(red)(-1))color(magenta)(+2)" describes"`

`f(x)" translated 1 unit to the right and 2 units vertically"`

`color(blue)"in general"`

`f(x+a)" movement of a units left"larr`

`f(x-a)" movement of a units right "rarr`

`f(x)+a" movement vertically up of a units "uarr`

`f(x)-a" movement vertically down of a units" darr`