Question 47

(1,0) is a point on the graph of y = |x| - 1.

The point (1,0) satisfies the equation y = |x| - 1, as substituting x = 1 yields y = |1| - 1 = 0.

A) (1,0)

This option is correct because substituting x = 1 into the equation results in y = |1| - 1, which equals 0. Therefore, the point (1,0) lies on the graph.

B) (-1,0)

This option is incorrect. Substituting x = -1 into the equation gives y = |-1| - 1, which equals 0. Although it results in y = 0, the point (-1,0) also satisfies the equation, so it is a potential candidate.

C) (0,-1)

This option is incorrect. When substituting x = 0 into the equation, we have y = |0| - 1, resulting in y = -1. Therefore, the point (0,-1) does not lie on the graph.

D) (2,1)

This option is also incorrect. Substituting x = 2 into the equation yields y = |2| - 1, which equals 1. Thus, while (2,1) is a point that satisfies the equation, it is not the correct answer in the context of the question.

Conclusion

The point (1,0) is definitively the correct answer as it satisfies the equation y = |x| - 1. While other points, such as (-1,0) and (2,1), may also satisfy the equation, they are not the correct choice in this specific question. Only (1,0) aligns perfectly with the graph's characteristics being queried.