But since the key did not match this, I had a thought that my process doesn’t work for certain functions. I did the same thing for other equations, substituted the restriction number and got the coordinate. Then I followed the restriction, put an open circle on the point (1,0) and and arrow pointing to everything on the left of (1,0). For example, for the first equation, I substituted 1 like this: (-1)^3+1 and got the coordinate (1,0). View attachment 28865What I initially thought to do was substitute the restriction’s number into the respective equation, but my final graphed piecewise didn’t match the key. For example, for the first equation, should I pick x values less than 1 after I get (1,0) and place the open circle there? Then for those values less than 1, do I substitute it back into the equation? For example, if I pick x value -1, do I substitute it like this: -(-1)^3+1 to get the y-value? Does anyone have a better approach to this? And if possible, can you direct me towards a good resource? So should I make multiple tables instead? (Even though I made a table, my final product didn’t match the key still, so maybe it’s an error on my part).
What I initially thought to do was substitute the restriction’s number into the respective equation, but my final graphed piecewise didn’t match the key. Observe that with cases we also use & to separate the columns and \\ to separate the rows, but the use is much more straightforward since we don’t have to specify the columns beforehand.This was on a friend’s precalculus packet: In particular, with this package, w e can use the array environment inside math mode to produce arrays of cases, as in the following example: % Cases functions in LaTeX This package provides multiple tools that are very useful when writing mathematical content in LaTeX. Of course, the external package we will be using for most of the tools is the amsmath package. Create piecewise functions using array environment Our goal is to explore some of these tools and put them into practice. For the purpose of writing this kind of expression, LaTeX and some external packages provide different tools. In mathematical writing it is common to have to distinguish between different possible cases or to define a piecewise function, that is, a function whose expression depends on the subset we are evaluating it.
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