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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.

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    $\begingroup$ 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. $\endgroup$ Jun 22, 2021 at 22:28
  • $\begingroup$ $f(x)$ 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. $\endgroup$
    – ndhanson3
    Jun 22, 2021 at 22:28
  • $\begingroup$ 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? $\endgroup$ Jun 22, 2021 at 22:28
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    $\begingroup$ It is not $f(x)$ which is a function of $x$, but $f$. $f(x)$ is the value of the function $f$ at $x$. $\endgroup$
    – Bernard
    Jun 22, 2021 at 22:30
  • $\begingroup$ @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 $x$". $\endgroup$ Jun 22, 2021 at 22:31

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I'm guessing you're currently in high school so without beating around the bush and/or being pedantic and asking you for definitions (which is futile as it is obvious you have this question because you don't know your definitions in the first place) and since you have an exam coming up very soon, I'll give you a straight answer.

$f(x)$ 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 $f(x)$.

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