The following sets of ordered pairs are functions. Give a
rule that could describe each function.
Please show your work.
A.{(5,3),(7,5),(11,9),(14,12)}
B. {(2,5),(3,10),(14,17),(5,26)}
To give a rule that describes each function, we need to find a pattern or relationship between the input values (x-values) and the output values (y-values) in each set of ordered pairs.
A. {(5,3),(7,5),(11,9),(14,12)}
In this set, we can see that the y-value is increasing by 2 for every increase of 2 in the x-value. So, we can write the rule as:
y = x + 1
B. {(2,5),(3,10),(14,17),(5,26)}
In this set, we can see that the y-value is obtained when the x-value is squared and 3 is added to it. So, we can write the rule as:
y = x^2 + 3
Explanation of finding the rule:
For set A:
We can observe that when the x-value increases by 2, the y-value increases by 2 as well. So, we can start by setting a rule where y = x + c. To find the value of c, we can check any ordered pair in the set. Let's take (5,3):
y = x + c
3 = 5 + c
c = 3 - 5
c = -2
So, the rule for set A is y = x - 2.
For set B:
We can observe that the y-value is obtained by squaring the x-value and adding 3 to it. So, we can start with the rule y = x^2 + c. To find the value of c, we can check any ordered pair. Let's take (2,5):
y = x^2 + c
5 = 2^2 + c
c = 5 - 4
c = 1
So, the rule for set B is y = x^2 + 1.