Question

write the equation that is the translation of y= |x| left 9 units and up 11 units.A) Y=|X+9|+11B) Y=|X-9| +11C) Y=|X-11|-9D) Y=|X+11|-9

Answer 1

We start with the function y=|x|.

If we translate the function 9 units to the left (negative side of the x-axis).

This means that the values of y that were for x, will happen for x+9, as we moved to axis to the right (or the function to the left).

We can test this with the value of y(0)=0. With the translated function, we have to have y=0 when x=-9, so f(-9)=|-9+9|=|0|=0.

Then,

`y=|x+9|`

Now, we translate the function 11 units up.

Then the value of the function is always 11 units up for every value of x. It can be done by adding a constant of value 11.

The function becomes:

`y=|x+9|+11`

Answer:

A) Y=|X+9|+11