Question

write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions. g(x) =

Explanation:

Step1: Identify the vertex

The vertex of the absolute - value function is at the point \((h,k)\). From the graph, the vertex is \((1,0)\), so \(h = 1\) and \(k = 0\).

Step2: Find the slope \(a\)

We can use a point on the graph to find \(a\). Let's take the point \((0,1)\). Substitute \(x = 0\), \(y = 1\), \(h = 1\), and \(k = 0\) into the equation \(y=a|x - h|+k\). We get \(1=a|0 - 1|+0\), which simplifies to \(1=a\times| - 1|\), so \(a = 1\).

Answer:

\(g(x)=1|x - 1|+0=|x - 1|\)