Function Table
X. Y
0.5. 2
1. 1
2. 0.5
4. 0.25
5
10
What is the function rule that represents the relationship between x and y.
looks like y = 1/x
And, to add to Steve's response, if it is y=1/x, then the product of xy is = 1.
Is xy a constant?
To determine the function rule that represents the relationship between x and y in the given table, we need to examine the pattern in the values.
Looking at the table, we can observe that as x increases, y decreases. Additionally, it appears that y is divided by 2 (or multiplied by 0.5) as x increases by a factor of 2.
By examining the pattern, we can infer that the function rule is a reciprocal relationship, where y is equal to a constant (let's call it k) divided by x. In other words, the function rule can be written as:
y = k / x
Now, we need to find the value of k by substituting any given x and y from the table into the function rule.
Using the first data point from the table (x = 0.5, y = 2), we can substitute these values into the function rule:
2 = k / 0.5
To find k, we can solve this equation:
2 * 0.5 = k
1 = k
So, the value of k is 1. Therefore, the function rule that represents the relationship between x and y in the given table is:
y = 1 / x