Graph y equals vertical bar x vertical bar minus 5.
Sure! To graph the function y = |x| - 5, we can start by plotting some points.
When x is positive, the absolute value function |x| is equal to x. So we can substitute positive values of x and calculate the corresponding y-values:
For x = 1, y = |1| - 5 = 1 - 5 = -4
For x = 2, y = |2| - 5 = 2 - 5 = -3
For x = 3, y = |3| - 5 = 3 - 5 = -2
When x is negative, the absolute value function |x| is equal to -x. So we can substitute negative values of x and calculate the corresponding y-values:
For x = -1, y = |-1| - 5 = 1 - 5 = -4
For x = -2, y = |-2| - 5 = 2 - 5 = -3
For x = -3, y = |-3| - 5 = 3 - 5 = -2
Now we can plot these points on a graph:
(-3, -2) | (-2, -3) | (-1, -4) | (1, -4) | (2, -3) | (3, -2)
| | | |
_______|_______|______|______|______|______|______
The graph for y = |x| - 5 is a V-shaped graph opening downwards with its vertex at (0, -5) and the arms extending to (-∞, -5) and (∞, -5).