which graph represents the function h(x) = |x - 3|?
which graph represents the function h(x) = |x - 3|?
Answer
Explanation:
Step1: Recall absolute - value function properties
The general form of an absolute - value function is (y = |x - h|), and its vertex is at the point ((h,0)). For the function (h(x)=|x - 3|), the vertex is at the point ((3,0)).
Step2: Analyze the behavior of the function
When (x\lt3), (h(x)=-(x - 3)=-x + 3), which is a line with slope (- 1). When (x\geq3), (h(x)=x - 3), which is a line with slope (1).
Answer:
The graph with the vertex at the point ((3,0)) and opening upwards (a V - shaped graph with the bottom of the V at ((3,0))) is the correct one. Without specific labels for the graphs, it's the graph where the lowest point of the V - shaped curve is on the x - axis at (x = 3).