"Help me translate this into
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,
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.