Expert: Sherry Wallin - 1/19/2011

Question
If f(4)=0 and f(6)=6, which of the following could represent f(x)?
a. 2/3x-4
b. x+2
c. x-4
d. 3/2x+6
e. 3x-12

Answer
Brittney~

f(4) = 0 is saying that you have an ordered pair of (4,0) and f(6) = 6 means there is an ordered pair (6,6) on a graph. There are a number of ways to determine which of the expressions describe f(x). One is to take the two points and figure out what f(x) is directly. The other is to plug in the x values and see if you get the y values in each of the ordered pairs and both must be true.

The first method is to find the slope:  m = (6-0)/(6-4) = 6/3 = 3. Now use the point slope form of a line to find the function that describes your points: y - y1 = m(x-x1) -> y - 0 = 3(x-4) and now simplify: y = 3x - 12. Thus e is your answer.

The second method we will use to check that (4,0) and (6,6) are actually true in f(x) = 3x-12:
f(4) = 3(4)-12 = 12-12 = 0 this one works. And finally f(6) = 3(6)-12 = 18-12 = 6 and this one works too!

Math Prof