# What is the domain and range of y=-absx-4?

Oct 2, 2016

Domain: $x \in \mathbb{R}$
Range: y ≤ -4

#### Explanation:

This will be the graph of $y = | x |$ that has been reflected over that opens downward and has had a vertical transformation of $4$ units.

The domain, like $y = | x |$, will be $x \in \mathbb{R}$. The range of any absolute value function depends on the maximum/minimum of that function.

The graph of $y = | x |$ would open upward, so it would have a minimum, and the range would be y ≥ C, where $C$ is the minimum.

However, our function opens downwards, so we will have a maximum. The vertex, or maximum point of the function will occur at $\left(p , q\right)$, in $y = a | x - p | + q$. Hence, our vertex is at $\left(0 , - 4\right)$. Our true "maximum" will occur at $q$, or the y-coordinate. So, the maximum is $y = - 4$.

We know the maximum, and that the function opens down. Hence, the range will be y ≤ -4.

Hopefully this helps!