the graph shows the function $f(x) = |x - h| + k$. what is the value of $h$?\n$\\bigcirc$ $h =…
the graph shows the function $f(x) = |x - h| + k$. what is the value of $h$?\n$\\bigcirc$ $h = -3.5$\n$\\bigcirc$ $h = -1.5$\n$\\bigcirc$ $h = 1.5$\n$\\bigcirc$ $h = 3.5$
Answer
Explanation:
Step1: Recall vertex form of absolute value function
The function ( f(x) = |x - h| + k ) has its vertex at ( (h, k) ). So we need to find the x - coordinate of the vertex of the given absolute - value graph.
Step2: Identify the vertex of the graph
Looking at the graph, the vertex (the point where the graph changes direction) is at ( x=-1.5 ) (by observing the grid, we can see that the minimum point of the V - shaped graph is at ( x = - 1.5)). Since the x - coordinate of the vertex of ( f(x)=|x - h|+k ) is ( h ), then ( h=-1.5 ).