The following sets of ordered pairs are functions. Give a
rule that could describe each function.
A.{(5,3),(7,5),(11,9),(14,12)}
B. {(2,5),(3,10),(14,17),(5,26)}
Did you not look at the solution I gave you earlier this morning???
http://www.jiskha.com/display.cgi?id=1345265420
well just wanted to see how you worked the answer
it is 17 not 7
To determine a rule that describes each function, we need to identify a pattern or relationship between the x-values and the corresponding y-values in each set of ordered pairs.
Let's analyze each function:
A. {(5,3),(7,5),(11,9),(14,12)}
The x-values in this set are increasing by 2 (from 5 to 7, then from 7 to 11, and finally from 11 to 14). Similarly, the y-values are increasing by 2 as well (from 3 to 5, then from 5 to 9, and finally from 9 to 12).
Based on this pattern, we can observe that for every x-value, the corresponding y-value is obtained by adding 2. Therefore, the rule that describes this function can be stated as:
y = x + 2
B. {(2,5),(3,10),(14,17),(5,26)}
In this set, the relationship between the x-values and y-values is not as straightforward as in the previous one. By examining the ordered pairs, we can see that the y-values are obtained by multiplying the x-values by different numbers and adding a constant term.
For example, when the x-value is 2, the corresponding y-value is 5. We can express this relationship as:
y = 2x + 1
When the x-value is 3, the corresponding y-value is 10, which can be described by:
y = 3x + 1
Similarly, when the x-value is 5, the corresponding y-value is 26:
y = 5x + 1
Lastly, when the x-value is 14, the corresponding y-value is 17. However, the previous rule of multiplying by x and adding one does not hold. Instead, we can try a different approach:
y = x - 1
Based on these patterns, we can conclude that the rule that describes this function can be written as a piecewise function:
y = 2x + 1 (when x is not equal to 14)
y = x - 1 (when x is equal to 14)
Note: It's important to note that there can be different rules that describe a given set of ordered pairs. The rules provided above are based on the patterns observed in the given functions.