Question

(1 point)

8. The ordered pairs (1, 2), (2, 4), (3, 8), (4,16), and (5,32) represent a function. What is a rule
that represents this function?
O y=x^2
O y=2x
O y=2^x
O y=x+2

Answer 1

9514 1404 393

Answer:

(c) y=2^x

Explanation:

You can check each of the offered functions to see which one fits. It is often informative to check the last of the offered points.

5^2 ≠ 32

2×5 ≠ 32

2^5 = 32 . . . . . a good candidate

5 +2 ≠ 32

Only the third choice matches the given ordered pairs.

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If you're trying to figure out the function, it is often useful to look at the differences between given values. The x-values differ by 1. The y-values differ by 2, 4, 8, 16. These are not constant, so the function is not linear (eliminates B and D). These differences don't have a common difference, so the function is not quadratic (eliminates A).

Both the y-values and their differences have a common ratio of 2, a strong indicator this is an exponential function with a base of 2 (matches C).