Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).

Express the polar equation \(r=\cos 2\theta\) in rectangular coordinates. Find the maximum height above the \(x\)-axis of the cardioid \(r=1+\cos \theta\text{.}\) Sketch the graph of the curve whose ...

Bar graphs seem like one of the simplest ways to represent data. Many people assume that the longer the bar, the bigger the number it represents. Sometimes bar graphs represent an average not a total ...