how do you get values out of this function: $y = f(x)$?

Question

How can I plug in a value for $x$ in $y = f(x)$ and get a result for $y$?

What does the $f$ do in the equation?

I know it stands for a function, but does it actually represent a value that I should plug in?

Answer 1

$f$ does indeed denote a function, and expressing it as $f(x)$ makes it clear that $f$ is a function of x.
$f$, or $y = f(x)$, does not represent a value you "plug in": rather, to evaluate the value of $y = f(x)$ at a given value of $x$, you need to "plug" that given value of $x$, say $a$, into $f(x)$; in other words, you need to evaluate $f(a)$.

More details:

$y = f(x)$ means that $y$ is a function of x. To evaluate the function for a given x, in order to determine the value of $y = f(x)$, you need to know the function:

e.g. Suppose $y = f(x)$ where $f(x) = x^2 +7$. Then, if you want to "plug in" a value for $\bf{x}$, (also known as "evaluating y or f(x) at a given value $x$), say "x = 3": that means for $x = 3$, we have $y = f(3) = 3^2 + 7 = 9 + 7 = 16$. f(x) and "y" are sometimes used interchangeably, but f(x) is more explicit about being a function of $x$.

"$x$" is the value at which you evaluate $y = f(x)$.

"$y$" is often used instead of f(x), when it's clear that $y$ is a function of $x$, especially, for example, when the y-coordinate of a set of points in the Cartesian plane is expressed as a function of the x-coordinates of the set of points.

Answer 2

Yes it does represent a value.

• Example if you take your $f(x)=x$ then when you plug in $1$, the output $y=f(1)=1$.

• If you take your $f(x)=x^{2}$, then when you plug $x=2$, your output is $2^{2}=4$.

• If you take $f(x)=|x|$, then when you put $x=-2$, your output is $|-2|=2$.

For more information, i suggest you to read this Wikipedia page: