Example A-9.1

Example A-9.2

Graph the (discontinuous) function $f\left(x\right)\&equals;\left\{\begin{array}{cc}2 x\&plus;1& x<2\\ 10-3 x& x\ge 2\end{array}\right.$ on the interval $\left[0\&comma;4\right]$.

Example A-9.3

Graph the curve defined parametrically by the equations $x\left(t\right)\&equals;2 t\&plus;1$, $y\left(t\right)\&equals;t^2-1$, for $-1\le t\le 1$.

Example A-9.4

Graph the curve (an ellipse) defined implicitly by the equation $3 x^2\&plus;5 y^2\&equals;7$.

Example A-9.5

Graph $x^3\&plus;2x^2-5x-9$ on the interval $\left[-3\&comma;3\right]$, and estimate the coordinates of intercepts and extrema graphically.

Example A-9.6

Create an animation showing how the number and location of the real zeros of the quadratic polynomial $x^2\&plus;b x\&plus;3$ vary with the parameter b.

Example A-9.7

Explore how the graph of the quadratic polynomial $a x^2\&plus;b x\&plus;c$ depends on each of the parameters a, b, c.

Example A-9.8

Graph a polygonal line through the points $\left(1\&comma;2\right)\&comma;\left(3\&comma;7\right)\&comma;\left(4\&comma;-2\right)$.

Example A-9.9

Graph $f\left(x\right)\&equals;\frac{x}{x-1}$, showing both its horizontal and vertical asymptotes.

Example A-9.10

Graph the vertical line segment between the points $\left(1\&comma;2\right)$ and $\left(1\&comma;5\right)$. Graph the vertical line $x\&equals;3$.