Observe the table of domains and ranges for a mysterious function. Given the table of values, what is the range for a domain of ?
Domain 

Range 

13 
352 

5 
56 

1 
4 

0 
1 

7 
92 

20 
781 
Source: mathcontest.olemiss.edu 6/30/2008
SOLUTION
We plot the given 6 data points to help us visualize the graph of the mysterious function. The plot seems to suggest that the function might be a quadratic function of the form .
Calculate
When :
Calculate and
When :
(1)
When :
(2)
Multiply Eq. (1) by and add it to Eq. (2) yields:
——————–
Substitute in Eq. (1) yields:
Equation of the function
So the equation of the function is
Check
When ?
. YES
When ?
. YES
We should also check the remaining 4 data points: .
Graph of the function
What is the value of the function when ?
.
Answer: .