Question

The ordered pairs (1,2),(2,4),(3,8),(4,16), and (5,32) represent a function?

a. y=x^2 b. y=2x c. y=2^x d. y=x+2****** The ordered pairs (1,16),(2,25),(3,36),(4,49), and (5,64) represent a function. What is a rule that represents this function?
a. y=x^2 b. y=x+15 c. y=2(x+3)*** d. y=(x+3)^2

Answer 1

I know the first one is b.

Answer 2

1. The answer for the first question is c.

2. The answer for the second question is d.

Explanation:

1. The idea to solve this exercise is to evaluate the given functions in the points {1,2,3,4,5} (notice that these are the x component of the ordered pairs) and then eliminate the different possibilities.

• The option a. cannot be because 1²=1, which is different from 2 (recall the ordered pair (1,2)).

• The option b. cannot be because 2*3=6, which is different from 8 (recall the ordered pair (3,8))
• The option c. is the answer, notice that 2¹=2, 2²=4, 2³=8, 2⁴=16 and 2⁵=32.
• The option cannot be, because 1+2=3, which is different from 2 (recall the pair (1,2)).

2. The idea is the same of the above.

• The option a. cannot be because 1²=1, which is different from 16 (recall the pair (1,16)).
• The option b. cannot be because 2+15=17, which is different from 25 (recall the pair (2,25)).
• The option c. cannot be because 2(1+3)=8, which is different from 16 (recall the pair (1,16)).
• By elimination this should be the correct answer. Anyway, it is no difficult to check that (1+3)²=16, (2+3)²=25, (3+3)²=36, (4+3)²=49 and (5+3)²=64.