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

Answer:

$y=(x+8)^{2}$

Step-by-step 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