Each value in the 'x' column (on the left) is unique. There are no repeated x values. This means we do have a function.
Put another way, each x value leads to exactly one y value. This is another way to see that we have a function. A function input must have one output or else it would lead to confusion or ambiguity. For example, let's say you wanted to convert from celsius to fahrenheit. You would use the conversion function F = (9/5)C+32. The idea is whatever celsius C value you plug in, you should get ONE and only one fahrenheit value. Otherwise, it would be impossible to know which fahrenheit temperature to go with.
Yet another way is to graph each (x,y) point and notice it is impossible to draw a single vertical line through more than one point mentioned in the table. This graph passes the vertical line test to further confirm that we do have a function.
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Answer: Yes, because every x-value corresponds to exactly one y-value
In other words, the answer is choice B
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<h3>3 answers: Choice A), Choice C), Choice D)</h3>
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Explanation:
We have a triangle with sides a,b,c where a = 3 and b = 3 are given. The side c is unknown, but using the variation of the triangle inequality theorem allows us to say the following:
b-a < c < b+a
3-3 < c < 3+3
0 < c < 6
The missing side c is between 0 and 6 units long, but cannot be equal to 0 and can't be equal to 6 either. Therefore, the answers must be A) 4, C) 5, and D) 2. All of these values satisfy the inequality 0 < c < 6.
Something like c = 12 is too large. I recommend cutting out two slips of paper that are 3 inches long, and you'll find it impossible to form a triangle that has a third side of 12 inches. The longest side you can form is 3+3 = 6 inches, but you wouldn't have a triangle at that point (it would be a straight line instead). This is a visual way to rule out choice E, and it also rules out choices B and F for similar reasoning.
The parallel lines have the same slope.
The formula of a slope:
We have the points (2, 5) and (6, -11).
Substitute:
4+3=12 3*3*3==27 12-27=-15 5*{-15}=-75
D, it’s the only answer that equals 30. When splitting up the 6, you’re doing the distributive property, which is what D is doing.
