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

1 Answer
Noah G
Oct 2, 2016

Domain: x in RR
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 RR. 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 (p, q), in y = a|x - p| + q. Hence, our vertex is at (0, -4). 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!

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