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# Which of the following equations is the translation 2 units left of the graph of y = |x|?

y = |x| - 2

y = |x - 2|

y = |x + 2|

# None of the above

**Solution:**

The function given is

y = |x|

As it is an absolute function, its transformation is

y = |x + a| + b

Where a is the horizontal shift and b is the vertical shift

The graph shifts a units left if a > 0

The graph shifts a units right if a < 0

The graph shifts b units up if b > 0

The graph shifts b units down if b < 0

Given - The graph translate 2 units left

Here a is 2 and b is 0

The function required is

y = |x + 2| + 0

y = |x + 2|

Therefore, the equation is y = |x + 2|.

## Which of the following equations is the translation 2 units left of the graph of y = |x|?

**Summary:**

y = |x + 2| is the translation 2 units left of the graph of y = |x|.

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