What is meant by $f(x)$ is function of $x$. Or $f(x)$ as a function of $y$?

I am so confused about the terminology and vocabulary here. I tried googling it but couldn't find anything satisfactory. I have a test tomorrow. I would be glad if someone could explain what this conceptually means.

• I don't think anyone can give a good answer in the answer box since "I am so confused" is not specific enough. I also do not know what f(x) as a function of y means. Jun 22, 2021 at 22:28
• $f(x)$ is a function of $x$ would be correct and it just means $f$ depends on $x$. Saying $f(x)$ is a function of $y$ would be wrong. Jun 22, 2021 at 22:28
• Do you want a full explanation of functional notation? What resources did you find? How about Khan Academy? How about MathBitsNotebook ? What is confusing you about the explanations you found? Jun 22, 2021 at 22:28
• It is not $f(x)$ which is a function of $x$, but $f$. $f(x)$ is the value of the function $f$ at $x$. Jun 22, 2021 at 22:30
• @ndhanson3 I disagree that "$f(x)$ is a function of $x$" is correct. That may be the usual phrase but it's not technically correct. One should simply say "$f$ is a function" and "$f(x)$ is the value of $f$ at $x$". Jun 22, 2021 at 22:31

$$f(x)$$ simply means the output value using the function $$f$$ when $$x$$ is the input value. For example: $$f(x)=2x+3$$ then for input value $$x=2$$, the output value using the function $$f$$ is $$f(2)=2(2)+3=7$$. You'd usually (conventionally) want to plot these output values of function $$f$$ on $$Y$$ axis and input values on $$X$$ axis on a graph paper. So we set $$y = f(x)$$. And hence, now $$y$$ is simply another name for $$f(x)$$.