"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 + v_{0} t + h_{0}

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 + v_{0} x + h_{0}

j(x) = g x + v_{0}

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.

Karen L.

03/29/14