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functions and formulas

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3 Answers

Karen,
           Given a function, say f(x)=4xthe instruction find f(-1) means to substitute -1 every where there is an x and do the indicated calculation. i.e. f(-1)=4*(-12) =4. This function is some times expresses as y=4x2 if you wanted to make a graph of the function. In this case you would select several values for x and calculate the corresponding y values and plot y vs x on a coordinate axis.
 
Jim

Comments

Then I was on the right track! y=fx I wrote the equation as f(-1) = -4(-1^)+2 ...so y ==2 and x=-1???
Here are a few results when f(x)=4x2
 
When x=-1, y=4.
When x=0, y=0.
When x=1, y=4.
When x=2, y=16.
 
I don't know what you guys are talking about right now. If you get time, do you mind posting again to explain? I get the feeling that the original problem was displayed incorrectly, or something like that.
Steve,
          The syntax of some of the problems that are posted leaves a lot to be desired. When I have a question about where the () should be I usually try and figure out from the context how the problem might make sense and proceed accordingly.
The original problem as posted is: "help me translate this into english please!!
f(x)=4x^+2;find f(-1) what is this asking? i know that f(x) is the same as y,correct? what do they mean by "find f(-1) are they asking to find x and y?"
I just assumed that f(x) =4x2 …..
 
Jim
Thanks, Jim. I understand that much. It is when I get to "f(-1) = -4(-1^)+2 ...so y ==2 and x=-1" that it stops making sense to me. I interpreted this to be:
f(-1) = 4(-1)2, with y=2 when x=-1, which is not correct, of course. 
Thanks for trying to explain.
They are saying that you need to substitute -1 everywhere there is an "x" in the problem. Here is how it works:
f(x) is pronounced "function of x" of course
f(-1) is pronounced "function of -1"
All this means is "what is y when x is (whatever)?" Well, y=4x^2 when the f(x) is x. When f(x) is actually f(-1), then y=4(-1)^2. If the f(x) is f(18), then y=4(18)^2
 
Please feel free to contact me if you have any questions. Thanks!
 

Comments

Where do you get the 18? I am totally confused..I get that you substitute the x for -1
Steve,Dont get the 4(18) you have an extra 2 in there..the original equation is:y(x)=-4x^+2;asking to find -1..(the x is squared...)
so if you say i substute a-1 where ever there is an x...then f(-1)= -4(-1^)+2,yes?...that would be -4(1) or -4 +2 which equals -2...
That's right Karen. Thanks for the catch! I will fix it. The 18 was an example. There has been some discussion among the tutors about using the actual problem, in case it is for homework, so I was attempting to provide an alternative. The +2 was a mistake. Thanks, Karen from Fremont NH!
 
"Help me translate this into English please!!
 
f(x) = 4x^(+2); find f(-1)
 
What is this asking? I know that f(x) is the same as y, correct? What do they mean by "find f(-1)", are they asking to find x and y?"
 
You're probably studying "Functional Notation".
 
The function f is defined as f(x) = 4x^2; but it could also be defined as any of these, and more:
f(a) = 4a^2,
f(b) = 4b^2,
f(c) = 4c^2,
...
etc.
 
The point is that the variable inside the parentheses of f(x) tells you what the independent variable is in 4x^2, which is the "rule" for f. That's why we read f(x) as "f of x"; f is a function of the independent variable x.
 
This is important when there are more letter numbers in the rule than just the independent variable, e.g.,
 
h(t) = (1/2) g t^2 + v0 t + h0
 
Here the function name is h and the independent variable is t; the other letters represent constants that are either given or need to be found.
 
"find f(-1)" means to substitute –1 for the independent variable in the rule for f.
So f(x) = 4x^2 becomes:
 
f(-1) = 4(-1)^2 = 4(-1)(-1) = 4.
 
"I know that f(x) is the same as y, correct?"
 
Not exactly. f(x) is a function that has a value for each value of x. If you want to see the relationship visually you would use an x-y coordinate plane and graph y = f(x). I.e., for every x-coordinate you would find the value of f(x) and use it as the y-coordinate. Each point you graph would be (x,f(x)).
 
However, we might want to graph multiple functions on the same x-y plane. E.g.:
 
h(x) = (1/2) g x^2 + v0 x + h0
 
j(x) = g x + v0
 
k(x) = g
 
The points we would graph would be: all (x,h(x)), all (x,j(x)), all (x,k(x)); where the y-coordinates are, respectively, y = h(x), y = j(x), y = k(x).
 
So "y =" tells us what axis we'll use to represent the function value.