the teacher told us to draw a graph from a function and I was having a hard time until I graphed it out on Desmos. This is the output:
Picture of the graph (the site won't let me upload the picture)
The teacher never taught us about a graph that splits like that and the only graph I know that splits similarly is Tan from trigonometry.
My question is what is the name of this type of graph and how do we know it is drawn like that without using any graphing calculator. Apologies for the bad english as it is not my main language. Thank you
Edit: What I meant by this type is, for example:
If the graph is U shaped, then it is a graph of a quadratic function
If the graph is a line, then it is a graph of a linear function.
I think the more correct wording for the question is What is the term used to call this graph?
Functions of the form $f(x) = \frac{p(x)}{q(x)}$, where $p$ and $q$ are polynomials, are called rational functions, just like how numbers of the form $\frac{p}{q}$ where $p$ and $q$ are integers are called rational numbers.
To know what the graph of a rational function will look like, some of the features include:
If $p(x)$ has a zero (and $q(x)$ doesn't), then $f(x)$ will have a zero at the same point.
If $q(x)$ has a zero (and $p(x)$ doesn't), then $f(x)$ will have a vertical asymptote at that point.
You can perform polynomial division to determine the leading behaviour of $f(x)$ as $x$ goes to $\pm \infty$. For example, $x^2 + 9x - 22 = (x-3)(x+12) + 14$, so as $x \rightarrow \pm \infty$, $\frac{x-3}{x^2 + 9x - 22}$ will start to look like the graph of $\frac{1}{x+12}$.