Question

Determine the vertex point, domain, and range of the following function
y = -|x| + 2

Answer 1

y = |x| is a v-shaped graph that opens up and have vertex (0, 0).
Now we need to see each change done to it.

y = -|x| makes every y-coordinate its additive inverse, so y = -|x| still has the vertex at (0, 0), but now is turned downward.

y = -|x| + 2 can be changed to

y - 2 = -|x|

Now y was replaced by y - 2. When y is replaced by y - k, the graph shifts vertically k units. In this case, k = 2, so the graph shifts up 2 units. The vertex is now at (0, 2).

Vertex: (0, 2)
Domain: all real numbers
Range: all real numbers less than or equal to 2.