Question

1. consider the graph of a function.

which two ordered pairs could be added to the coordinate plane so that the graph remains a function?

a (-5, 1)

b (-1, 0)

c (0, 2)

d (1, -2)

e (2, 2)

Explanation:

Step1: Recall Function Definition

A function is a relation where each input (x - value) has exactly one output (y - value). So, we need to check for each option if the x - value of the ordered pair is already associated with a y - value in the given graph.

Step2: Analyze Option A: (-5, 1)

Check the x - value - 5. From the graph, there is no point with x=-5. So, adding (-5, 1) will not violate the function definition.

Step3: Analyze Option B: (-1, 0)

Check the x - value - 1. From the graph, there is a point with x = - 1 (the point with y - value around 1). So, adding (-1, 0) would mean x=-1 has two y - values (1 and 0), which is not allowed in a function.

Step4: Analyze Option C: (0, 2)

Check the x - value 0. From the graph, there is a point with x = 0 (the point with y - value 4). So, adding (0, 2) would mean x = 0 has two y - values (4 and 2), which is not allowed in a function.

Step5: Analyze Option D: (1, - 2)

Check the x - value 1. From the graph, there is a point with x = 1 (the point with y - value 5). So, adding (1, - 2) would mean x = 1 has two y - values (5 and - 2), which is not allowed in a function.

Step6: Analyze Option E: (2, 2)

Check the x - value 2. From the graph, there is a point with x = 2 (the point with y - value 8). So, adding (2, 2) would mean x = 2 has two y - values (8 and 2), which is not allowed in a function.

Answer:

A. \((-5, 1)\)