2.2.3 *args & **kwargs

2.2.3 *args & **kwargs

Introduction

args and kwargs are used to pass arguments to a function. args is used to pass a variable number of positional arguments to a function, and kwargs is used to pass a variable number of keyword arguments to a function.

args

args is used to pass a variable number of positional arguments to a function. It is a tuple.

kwargs

kwargs is used to pass a variable number of keyword arguments to a function. It is a dictionary.

Example 1

Sketch and analyze $y = -x^2 - 2x + 3$.

Solution

$y$-intercept: $y = 3$ when $x = 0$.

$x$-intercepts: solve $-x^2 - 2x + 3 = 0$, or $x^2 + 2x - 3 = 0$:

Vertex:

So the vertex $(-1, 4)$ is a maximum point. The function is increasing on $(-\infty, -1)$ and decreasing on $(-1, \infty)$.

Finding Maximum and Minimum Values by Completing the Square

Completing the square rewrites $f(x) = ax^2 + bx + c$ in vertex form. It is a dictionary.

Example 3

Find the maximum or minimum value of $f(x) = x^2 - 2x - 3$.

Solution

Here $a = 1$, $b = -2$, $c = -3$:

Since $a = 1 > 0$, the minimum value of $f$ at $x = 1$ is $-4$.