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).

👉 Learn how to graph the reciprocal function. A reciprocal function is a rational function whose expression of the variable is in the denominator. A reciprocal function is of the form f(x) = a / (x + ...

Learn how to sketch angles in terms of pi. An angle is the figure formed by two rays sharing the same endpoint. Angle is measured in radians or in degrees. One complete revolution about a point is ...

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 ...