Tutorial: Analyzing graphs
Game version
(This topic is also in Section 12.4 in Finite Mathematics and Applied Calculus) #[I don't like this new tutorial. Take me back to the older tutorial!][No me gusta este nueve tutorial. ¡Regresame al tutorial más viejo (solo en inglés)!]#

Resources
Function evaluator and grapher  Excel grapher 
Features of graphs
It is easy enough to use graphing technology to draw a graph, but we need to use calculus to understand some of the features we are seeing and tell us where to look, and also to help us draw a curve by hand without technology.
To illustrate this point, take a look at the following graph, which has all kinds of interestinglooking features shown with different colors and markers. Each of the buttons shows a particular feature, as listed below.
Features of the graph of $\bold{y = f(x)}$
 x and yintercepts : $x$intercepts: In the equation $y = f(x)$, set $y=0$ and solve for $x$.
$y$intercepts: In the equation $y = f(x)$, set $x=0$ and solve for $y$.  Maxima and minima : Use the techniques of the %%maxmintut to locate and classify the absolute and relative maxima and minima.
 Points of inflection : Use the techniques of the %%inflectiontut to locate and classify the points of inflection.
 Behavior near singular points of $\bold{f}$ : If $a$ is a singular point of $f$, consider $\lim_{x \to a^}f(x)$ and $\lim_{x \to a^+}f(x)$ to see how the graph of $f$ behaves as $x \to a$.
 Behavior at infinity : Consider $\lim_{x \to \infty}f(x)$ and $\lim_{x \to \infty}f(x)$ to see how the graph of $f$ behaves far to the left and right.
Now try the exercises in Section 12.4 in Finite Mathematics and Applied Calculus.
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