Is it wrong to represent a dependent variable and a function using the same symbol? For example, can we write the parametric equations of a curve in xy-plane as $x=x(t)$ , $y=y(t)$ where $t$ is the parameter? For me function is different from dependent variable. But, in many calculus texts, sometimes, a dependent variable and a function are represented using the same symbol, why?
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When we write $y=f(x)$, we give names to the function, its input, and its output.
But not all of these names are needed at all times.
What if we want to give names to the input and output, but not to the function itself? Writing $y=\cdot (x)$ is typographically awkward. Writing $y=y(x)$ conveys as much information, and is less likely to be mistaken for a typo. I think "$x\mapsto y$" would be a better choice, but this is less common.