I am working on transforming a graph. The problem I am having is the equation is different than what I am use to and I could use some help understanding how to read the function. I understand $f(x)=x$. The x in this function is the independent variable, and the $f(x)$ is the y value or is the dependent variable. Two coordinates on a graph would be:
$$ \begin{array}{c|c|c|} & \text{x} & \text{y} \\ \hline \text{coordinates} & 1 & 1 \\ \hline \text{coordinates} & 2 & 2 \\ \hline \end{array} $$
I put a value in the function for x and then the function spits out a value for y.
The function I am working on looks like there are two y values. $y=f(1/2x)$. Are there two ys and no x coordinates? I also have to transform the a graph by using the reciprocal. Why do I use the reciprocal? Looking at this equation I would think the graph coordinates would be $$ \begin{array}{c|c|c|} & \text{x} & \text{y} \\ \hline \text{coordinates} & 1 & 1/2 \\ \hline \text{coordinates} & 2 & 1 \\ \hline \end{array} $$
It is the opposite of what I think and I am not sure why. Here is what the book is telling me to do $$ \begin{array}{c|c|c|} & \text{x} & \text{y} \\ \hline \text{coordinates} & 1 & 2 \\ \hline \text{coordinates} & 2 & 4 \\ \hline \end{array} $$
I am not really sure why the reciprocal is being used and think it probably has to do with how the equation is written.