Question

Which graph represents the function g(x) = |x + 4| + 2?

On a coordinate plane, an absolute value graph has a vertex at (negative 4, 2).

On a coordinate plane, an absolute value graph has a vertex at (negative 2, 4).

On a coordinate plane, an absolute value graph has a vertex at (4, 2).

On a coordinate plane, an absolute value graph has a vertex at (2, 4).

Answer 1

Vertex is at (-4,2)

Explanation:

See the attached graph. The absolute value operation has the effect of not allowing a y value of less than 2.

The term Ix+4I results in a minimum value of 0, which occurs when x = -4. Values less than -4 result in increasing values since the absolute funtion makes everything positive. So for x = -10, for example, the result is I-6I or +6. The full fi=unction add +2, so the minumum value of y is 2. This is also the vertex: (-4,2). See the graph.