the graph shows ( g(x) ), which is a transformation of ( f(x)=|x| ). write the function rule for ( g(x)…
the graph shows ( g(x) ), which is a transformation 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 fractions.\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. From the graph, the vertex of (g(x)) is ((h = 0,k = 0)). So the function is of the form (g(x)=a|x - 0|+0=a|x|).
Step2: Find the value of (a)
We can use a point on the graph to find (a). Let's take the point ((2,1)) (since when (x = 2), (y = 1)). Substitute (x = 2) and (y = g(2)=1) into (g(x)=a|x|). We get (1=a|2|), so (a=\frac{1}{2}).
Answer:
(g(x)=\frac{1}{2}|x|)