Question

1) The graph shows y as a function of x Suppose a point is added to this graph. Which choice gives a point that preserves the function?

A) (5,5)
B) (0,9)
919.-1)
D) (2.-4

Answer 1

None of the given choices preserves the function represented by the graph.

Step-by-step explanation:

To preserve the function represented by the graph, we need to find a point that lies on the graph. A point on the graph satisfies the relationship between x and y shown on the graph. From the given answer choices, we need to find a point that lies on the graph and maintains the same relationship between x and y. Let's analyze each choice:

• Choice A: (5,5) - This point does not lie on the graph.
• Choice B: (0,9) - This point does not lie on the graph.
• Choice C: (-1,9) - This point does not lie on the graph.
• Choice D: (2,-4) - This point does not lie on the graph.

None of the given choices preserves the function represented by the graph. Therefore, none of the choices is correct.

Answer 2

Answer: B) (0,9)

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Step-by-step explanation:

The points on the given graph are:

• (-7,4)
• (-3,-3)
• (2,9)
• (3,-8)
• (5,7)
• (9,3)

Notice that the slightly darker grid lines indicate 5 on either x or y axis. This helps visually spot where the points are fairly quickly. Though admittedly, it would be better if your teacher provided numbers on the x and y scales.

Now if we were to add something like point A(5,5) to the graph, then this function would cease to be a function. This is because the points (5,7) and (5,5) fail the vertical line test. The input x = 5 leads to the outputs y = 5 and y = 7 at the same time. A function is only possible if any x input leads to exactly one y output only.

So this is why we eliminate choice A from the possible answer pool.

Choice C is a similar story. The two points (9,3) and (9,-1) fail the vertical line test this time, i.e. the input x = 9 has multiple outputs y = 3 and y = -1 simultaneously. We rule out choice C.

Choice D is also ruled out because of (2,-4) and (2,9) failing the vertical line test.

We're left with choice B. Luckily, adding the point (0,9) to the mix does not break the function. The input x = 0 wasn't part of the original function.

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In short, we eliminate choices A,C and D because they fail the vertical line test. Choice B does not fail the vertical line test so it's the final answer.