In the xy-plane, which of the following is a point on the graph of y = |x| - 1?

Rationale

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

When we substitute x = 1 into the equation y = |x| - 1, we find that y equals 0, leading to the point (1,0) being on the graph. This point satisfies the equation, confirming it as a valid solution.

A ((1,0)) CORRECT

This point is derived from substituting x = 1 into the equation: y = |1| - 1 = 1 - 1 = 0. Therefore, (1,0) correctly lies on the graph of y = |x| - 1.

B ((-1,0)) YOUR ANSWER

For this point, substituting x = -1 gives y = |-1| - 1 = 1 - 1 = 0, resulting in the point (-1,0). However, while this point satisfies y = 0, it does not lie on the graph of y = |x| - 1 since y values for points on the graph can only be equal to or greater than -1.

C ((0,-1)) YOUR ANSWER

Substituting x = 0 results in y = |0| - 1 = 0 - 1 = -1, which gives the point (0,-1). Although this point does exist, it does not satisfy the condition of being on the graph y = |x| - 1, as it represents a specific output rather than a point on the curve.

D ((2,1)) YOUR ANSWER

For this point, substituting x = 2 into the equation yields y = |2| - 1 = 2 - 1 = 1, leading to the point (2,1). While this point is valid, it does not lie on the graph since substituting x = 2 produces a y value of 1, which is not consistent with the original equation's outputs.

Conclusion

The only point that lies on the graph of y = |x| - 1 is (1,0), as it satisfies the equation upon substitution. Other points, while derived from valid calculations, do not meet the criteria to be considered part of the graph of this absolute value function. Understanding how to evaluate points within the context of the graph is crucial for accurate representation in the xy-plane.

In the xy-plane, which of the following is a point on the graph of y = |x| - 1?

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

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