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Question 330410: i was studying for the ACT compass test and i am having problems with functions. the question was: if f(4)=0 and f(6)=6 then which of the following could represent f(x)? The answer is 3x-12, but i do not understand how to get to that answer, what does the 4 and 6 have to do with it? thank you ahead of time
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Hint: If f(4)=0, then we have the point (4,0). Recall that f(x) is really 'y'. So if f(4)=0, then x=4 and y=0. Similarly, if f(6)=6, then we have the second point (6,6)
Answer by Edwin McCravy(20056)  (Show Source):
You can put this solution on YOUR website!
Do you know what f(4) and f(6) means? Apparently not.
f(4) means what you get when you substitute (4) for x in the right side of
f(x) = 3x-12
If you put a (4) wherever the x is you get
f(4) = 3(4)-12 and if you simplify the right side you get
f(4) = 12-12
or
f(4) = 0
---
Similarly, f(6) means what you get when you plug 6 in for x in
the right side of
f(x) = 3x-12
If you put a (6) wherever the x is you get
f(6) = 3(6)-12 and if you simplify the right side you get
f(6) = 18-12
or
f(6) = 6
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Now if you tried doing those two substitutions in any of the other
choices you had on your test you would not get 0 for f(4) and also
6 for f(6).
Learn that "f( )" with a number in the parentheses means
to substitute whatever number is in the parentheses for x into
the right side of the equation which has "f(x) = ____" where the
right side is some algebraic expression that contains x, such as
3x-12 or 6x-3 or 7x+3 or 8x²+3x-9 or etc. etc. etc. Then after
substituting, then simplify, and the number you get is equal
to f(that number)
Edwin
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