Question

The table of values shows the output values of three different equations for the same

Answer 1

Answer:

1. x+3
2. 3x^2
3. 3^x

Step-by-step explanation:

Relationship 1

The y-values have a common difference of 1, so the relationship is linear with as slope of 1. The only matching choice is (x+3), which matches the values of y1.

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Relationship 2

The y-values have differences that increase with a common difference. They are (3-0) = 3, (12-3) = 9, (27-12) = 15, (48 -27) = 21. The second differences are (9-3) = 6, (15-9) = 6, and so on with all second differences being 6. This tells you that a second-degree polynomial can model this sequence. The only matching choice is (3x^2), which matches the values of y2.

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Relationship 3

The y-values have increasing differences that also have increasing differences. The values have a common ratio of 3, indicating an exponential function will model this sequence. The only matching choice is (3^x), which matches the values of y3.