Question

The ordered pairs (1, 81), (2, 100), (3, 121), (4, 144), and (5, 169) represent a function. What is a rule that represents this function?

y = x^8

y = 8^x

y = (x + 8)^2

y = 8x ...?

Answer 1

`y=(x+8)^(2)`

Explanation:

we have that

The ordered pairs
`(1, 81), (2, 100), (3, 121), (4, 144)`, and
`(5, 169)` represent a function

The rule that that represent this function is equal to

`y=(x+8)^(2)`

Verify

For
`x=1` -----> Find the value of y in the equation

`y=(1+8)^(2)=81` -----> is correct

For
`x=2` -----> Find the value of y in the equation

`y=(2+8)^(2)=100` -----> is correct

For
`x=3` -----> Find the value of y in the equation

`y=(3+8)^(2)=121` -----> is correct

For
`x=4` -----> Find the value of y in the equation

`y=(4+8)^(2)=144` -----> is correct

For
`x=5` -----> Find the value of y in the equation

`y=(5+8)^(2)=169` -----> is correct

Answer 2

To determine what function is the correct answer we use the choices listed above to substitute x and obtain the value of y and see if it corresponds to the given y value. We do as follows:

y = x^8
y = (1)^8
y = 1 ----> NOT THE ANSWER

y = 8^x
y = 8^(1)
y = 8---> NOT THE ANSWER

y = (x + 8)^2
y = (1+8)^2
y = 81

y = 8x
y = 8(1)
y = 8 ---> NOT THE ANSWER