The ordered pairs (0,1) (1,4) (2,16) (3,64) and (4,256) represent a function. What is a rule that represents that function?
a) y=4^x
b) y=4x
c) y=x^4
d) y=x+4
i dont know how to do it please explain it and give the answer
the 1st pair is (0,1) ... that eliminates b), c), and d)
1 does not equal 4 times 0
1 does not equal 0^4
1 does not equal 0 plus 4
To determine the rule that represents the given function, we need to look for a pattern in the provided ordered pairs. Let's examine the y-values and the corresponding x-values:
(0,1) → y = 1
(1,4) → y = 4
(2,16) → y = 16
(3,64) → y = 64
(4,256) → y = 256
Looking at the pattern, we notice that the y-values are related to the x-values. Specifically, the y-values are obtained by squaring the x-values.
So, the rule that represents the function is y = x^2.
Now, let's compare this rule with the options provided:
a) y = 4^x
b) y = 4x
c) y = x^4
d) y = x + 4
The option that matches our rule is c) y = x^4.
Therefore, the rule that represents the given function is y = x^4.