the graph shows ( g(x) ), which is a translation of ( f(x)=|x| ). write the function rule for ( g(x)…

the graph shows ( g(x) ), which is a translation of ( f(x)=|x| ). write the function rule for ( g(x) ).\nwrite your answer in the form ( a|x - h|+k ), where ( a ), ( h ), and ( k ) are integers or simplified\nfractions.\n( g(x)= )

Answer

Explanation:

Step1: Recall the vertex form of absolute - value function

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

Step2: Identify the vertex ((h,k))

From the graph, the vertex of (g(x)) is ((- 2,0)), so (h=-2) and (k = 0).

Step3: Find the value of (a)

We can use another point on the graph to find (a). The (y) - intercept of (g(x)) is ((0,2)). Substitute (x = 0), (y = 2), (h=-2), and (k = 0) into (y=a|x - h|+k). We get (2=a|0-(-2)|+0), which simplifies to (2 = 2a). Solving for (a), we divide both sides by (2): (a = 1).

Answer:

(g(x)=|x + 2|)