Question

which equation represents the function graphed on the coordinate plane? \\( \bigcirc \\ g(x) = |x + 1| + 3 \\) \\( \bigcirc \\ g(x) = |x + 3| - 1 \\) \\( \bigcirc \\ g(x) = |x - 1| + 3 \\) \\( \bigcirc \\ g(x) = |x + 3| + 1 \\)

Explanation:

Step1: Identify vertex of graph

The vertex of the V-shaped graph is at (1, 3).

Step2: Recall absolute value form

The vertex form of an absolute value function is \( g(x) = |x - h| + k \), where (h, k) is the vertex.

Step3: Substitute vertex values

Substitute h = 1 and k = 3 into the form: \( g(x) = |x - 1| + 3 \).

Step4: Match with options

The result matches option C.

Answer:

C. \( g(x) = |x - 1| + 3 \)