Algorithm X.1: Graphing linear polynomials

Input: a linear polynomial $y = a_1x + a_0$ and an interval $[x_0, x_1]$.
Output: a graph.

Describe an algorithm for plotting a linear polynomial $y = a_1 x + a_0$ on the interval $[x_0, x_1]$. Your graph should identify both roots, the $y$ intercept, and the value of the polynomial at each end point.

Algorithm X.2: Graphing quadratic polynomials

Input: a quadratic polynomial $y = a_2 x^2 a_1 x + a_0$ and an interval $[x_0, x_1]$.
Output: a graph.

Describe an algorithm for plotting a quadratic polynomial $y = a_2 x^2 + a_1 x + a_0$ on the interval $[x_0, x_1]$. Your graph should identify roots, the extreme point, the $y$ intercept, and the value of the polynomial at each end point.

Algorithm X.3: Graphing cubic polynomials

Input: a cubic polynomial $y = a_3 x^3 + a_2 x^2 a_1 x + a_0$ and an interval $[x_0, x_1]$.
Output: a graph.

Describe an algorithm for plotting a cubic polynomial $y = a_3 x^3 + a_2 x^2 + a_1 x + a_0$ on the interval $[x_0, x_1]$. Your graph should identify roots, extreme points, the inflection point, the $y$ intercept, and the value of the polynomial at each end point.

Algorithm X.4: Graphing trigonometric functions

Input: an interval $[x_0, x_1]$.
Output: a graph.

Describe an algorithm for plotting the $y = \sin(x)$ function on the interval $[x_0, x_1]$. Your graph should identify roots and extreme points.

Input: an interval $[x_0, x_1]$.
Output: a graph.

Describe an algorithm for plotting the $y = \sin(2 \pi x)$ function on the interval $[x_0, x_1]$. Your graph should identify roots and extreme points.

Input: an interval $[x_0, x_1]$ and an angular frequency $\omega > 0$.
Output: a graph.

Describe an algorithm for plotting the $y = \sin(\omega x)$ function on the interval $[x_0, x_1]$. Your graph should identify roots and extreme points. Here $\omega$ is the angular frequency of the sine function.

Algorithm X.5: Graphing products of functions

Describe an algorithm for plotting $y = e^x \sin(4 \pi x)$ on the interval $[x_0, x_1]$. Hint: Plot $y = e^x$ and $y = -e^x$ first.

Describe an algorithm for plotting $y = x^2 \cos(4 \pi x)$ on the interval $[x_0, x_1]$. Hint: Plot $y = x^2$ and $y = -x^2$ first.