Which of the following describes the translation of y = |x| to y = |x + 7| - 2
y = |x| translated 2 units to the left and 7 units down
y = |x| translated 7 units to the right and 7 units down
y = |x| translated 2 units to the right and 7 units up
y = |x| translated 7 units to the left and 2 units down

Solution:

Given: Parent function is y = |x|

The translated function is

y = |x + 7| - 2

f(x) = f(x ± k) ± C

Where k denotes the number of units for translation in the x-axis

C denotes the number of units for translation in the y-axis

We can observe that there is x + 7 on the x-axis.

So the function is shifted left side by 7 units and -2 is added to the y-value

It is shifted downward by 2 units

Therefore, y = |x| translated 7 units to the left and 2 units down describes the translation.

Which of the following describes the translation of y = |x| to y = |x + 7| - 2

Summary:

The translation of y = |x| to y = |x + 7| - 2 is described by y = |x| translated 7 units to the left and 2 units down.