# Question #c4eca

Dec 28, 2017

#### Explanation:

As,$g \left(x\right) = | x | - 2 \mathmr{and} f \left(x\right) = | x |$
So,$g \left(x\right) = f \left(x\right) - 2$,it is the relation between$g \left(x\right) \mathmr{and} f \left(x\right) \textcolor{b l u e}{\left(A n s .\right)}$
Again,$g \left(x\right) = | x - 4 | \mathmr{and} f \left(x\right) = | x |$
Thus,$g \left(x\right) = | f \left(x\right) - 4 | \textcolor{red}{\left(A n s .\right)}$

Dec 28, 2017

See explanation.

#### Explanation:

$g \left(x\right) = | x | - 2$ vs. $f \left(x\right) = | x |$
The $- 2$ at the end of $g \left(x\right)$ represents a vertical shift of 2 units down. Take the graph of $f \left(x\right)$ and shift the whole thing down 2 units. This doesn't change the shape of the graph, just the location.

$g \left(x\right) = | x - 4 |$ vs. $f \left(x\right) = | x |$
The $- 4$ inside the absolute value of $g \left(x\right)$ represents a shift of 4 units to the right. Take the graph of $f \left(x\right)$ and shift the whole thing 4 units to the right. Again, this doesn't change the shape, just changes the location.