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Determine whether each point lies on the graph of the equation.y = |x - 2] + 5(a) (5,8)Yes, the point is on the graph.No, the point is not on the graph.(b) (-2, 0)0 Yes, the point is on the graph.No, the point is not on the graph.

User Mariobros
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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.

User Ubreddy
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