We have to find the values for the function:
y = | x - 2 | + 5 [1],
a) When x = 5, and check if the result is y = 8.
b) When x = -2, and check if the result is y = 0.
The function | x | is called absolute value function. And, for this function, we have that:
| x | = x
| -x | = x
Having all this information, we are ready to solve the question:
a) When x = 5, we have
y = | x - 2 | + 5
y = | 5 - 2 | + 5
y = | 3 | + 5
y = 3 + 5
y = 8.
Since we have that y = 8 when x = 5, the point is on the graph represented by the function [1]. Conclusion: the point (5, 8) is on the graph.
b) We can follow the same procedure as before:
When x = -2, we have
y = | x - 2 | + 5
y = | -2 - 2 | + 5
y = | -4 | + 5
y = 4 + 5
y = 9
Thus, for x = -2, the value for y = 9. We have the point (-2, 9), and not the point (-2, 0).Therefore, the point (-2, 0) is not on the graph.