Question

Q 1 Graph the functionY = |X+2| -3

Answer 1

The graph of y = |x+2| -3 is shown below:

Answer 2

First of all we know the Absolute Value Function that is:

$\left | x \right |= \left \{ {{x \ \ \ \ x \geq 0} \atop {-x \ \ \ \ x\ \textless \ 0}} \right.$

This is called the Parent Function of the Absolute Value Function.

From the equation:

$y=\left | x+2 \right |-3$

The term:

$\left | x+2 \right |$

means that the the Parent Function is shifted two units to the left.

On the other hand, the term:

$-3$

means that the function $\left | x+2 \right |$ is shifted three units downward. So the result is the graph shown below

Conclusion: The graph is the second one.