Answer:
Starting from the x-value (A column) for -7 and going down the y-values values (B column) are 5, 4, 3, 2, 1, 0, 1, 2
Explanation:
The function is given to us in the B column. We can use this to find the y-values without having to plug them in each time.
Finding the Vertex
In absolute value functions, there is a vertex. The vertex, in this case, is the minimum where the y-values change from decreasing to increasing. The absolute value formula is y = a|x - h| + k.
The vertex is equal to (h,k). The h-value in the function above is -2 and the k-value is 0. Thus, the vertex is at (-2,0).
Finding Slope
The slope of an absolute value function is written before the x. Since there isn't anything before the x in this function, the slope must be 1. So, the values either increase or decrease by 1.
Like all positive absolute value functions, the graph will decrease, reach 0, then begin to increase. The graph will reach 0 at the vertex.
Writing Out the Values
The table shows us that the y-values begin at 6. Then, we decrease by one until we get to 0.
- So, the first values are 6, 5, 4, 3, 2, 1, 0
Each of these x-values matches up with one of the y-values. Then, the graph begins to increase once again.
- The next values are 1 and 2
So together the y-values for the x-values -8 through 0 are 6, 5, 4, 3, 2, 1, 0, 1, 2.