which could be the graph of f(x) = |x - h| + k if h and k are both positive?
which could be the graph of f(x) = |x - h| + k if h and k are both positive?
Answer
Explanation:
Step1: Recall 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. For the function (f(x)=|x - h|+k) with (a = 1), (h>0) and (k>0), the vertex of the graph is the point ((h,k)) which is in the first quadrant since both (h) and (k) are positive.
Step2: Analyze the shape of the absolute - value graph
The graph of (y = |x|) has a "V" shape with the vertex at the origin ((0,0)). The graph of (y=|x - h|+k) is a translation of the graph of (y = |x|). The graph of (y = |x|) is shifted (h) units to the right and (k) units up.
Answer:
The graph with the vertex in the first quadrant (a "V" - shaped graph whose lowest point is in the first quadrant)