Write an equation for the translation of y = |x|.

Question

10.5 units left

y = |x| – 10.5

y = |x + 10.5|

y = |x| + 10.5

y = |x – 10.5|

Answer 1

To translate the graph of \( y = |x| \) 10.5 units to the left, you need to replace \( x \) with \( x + 10.5 \) in the equation. This is because adding a value inside the absolute value expression shifts the graph to the left.

So, the correct equation for the translation of \( y = |x| \) 10.5 units to the left is:

\[ y = |x + 10.5| \]

Thus, the correct answer is:

y = |x + 10.5|