{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b232e068",
   "metadata": {},
   "source": [
    "# Functions\n",
    "\n",
    "Consider the expression `2 + 2`: whatever line of code it appears on, we evaluate it in its entirety before using it.\n",
    "\n",
    "For example, `x = 2 + 2` stores the _result of_ the `2 + 2` expression, rather than the expression itself. Thus, `x` now contains the value $4$.\n",
    "\n",
    "What if we wanted to do something more complicated than a simple arithmetic equation?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "edc335d1",
   "metadata": {},
   "source": [
    "Let's take as an example a simple arithmetic equation: $2x + 1$. In Math, we might want to reference this equation elsewhere by saying that we should consider $f(x)$ to be that formula. Thus, everwhere we see $f(x)$, it's actually $2x + 1$. This allows us to plug in arbitrary values and build up results:\n",
    "\n",
    "$f(x) = 2x + 1\\\\\\text{let }x = 4\\\\f(4) = 9$\n",
    "\n",
    "We can do the same thing in programming, using \"**functions**\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "59999bc2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dcac813f",
   "metadata": {},
   "outputs": [],
   "source": [
    "len(\"hello\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "750044b2",
   "metadata": {},
   "outputs": [],
   "source": [
    "len(\"\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6cf3ea60",
   "metadata": {},
   "outputs": [],
   "source": [
    "math.sqrt(9)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fa140b9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "math.sqrt(7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "73d968e4",
   "metadata": {},
   "outputs": [],
   "source": [
    "range(1, 5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "364f99eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "range(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "47b07952",
   "metadata": {},
   "outputs": [],
   "source": [
    "math.sin(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1f049b3c",
   "metadata": {},
   "outputs": [],
   "source": [
    "str(17)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aa497c36",
   "metadata": {},
   "source": [
    "Function call examples:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a965a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 8\n",
    "y = 16\n",
    "z = math.sqrt(16)\n",
    "u = math.sqrt(y)\n",
    "v = math.sqrt(8 + 8)\n",
    "w = math.sqrt(x + x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25b3a9ef",
   "metadata": {},
   "source": [
    "## Defining a new function\n",
    "\n",
    "Instead of $f(x) = 2x + 1$, we're going to **def**ine a new body of code, and give it the name `dbl_plus`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aa14cf38",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dbl_plus(x):\n",
    "    return 2 * x + 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d053afa0",
   "metadata": {},
   "source": [
    "We can then use (or \"call\") that code thusly:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "16a78899",
   "metadata": {},
   "outputs": [],
   "source": [
    "dbl_plus(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5a11577a",
   "metadata": {},
   "outputs": [],
   "source": [
    "dbl_plus(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3a1b34b",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 346\n",
    "dbl_plus(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cef5d0da",
   "metadata": {},
   "source": [
    "## Practice Reading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "927cb53e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 1\n",
    "z = 3.1\n",
    "\n",
    "def multiply(x, y):\n",
    "    # (1) What are the values of x and y here\n",
    "    #     the first time multiply is called?\n",
    "    print(\"x,y:\", x, y)\n",
    "    z = 0\n",
    "    return x * y\n",
    "\n",
    "x = 2\n",
    "y = 1\n",
    "result = multiply(3, y)\n",
    "print(y)      # (2) What is the value of y here?\n",
    "result = multiply(x, 4)\n",
    "print(result) # (3) What is the value of result here?\n",
    "print(z)      # (4) What is the value of z here?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e677f087",
   "metadata": {},
   "outputs": [],
   "source": [
    "def multiply(x, y):\n",
    "    print(\"x,y:\", x, y)\n",
    "    z = 0\n",
    "    return x * y\n",
    "\n",
    "x = 2\n",
    "y = 1\n",
    "result = multiply(3, 4)\n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "572e09d8",
   "metadata": {},
   "source": [
    "## More Definition Examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "33d8aed7",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dbl_plus(x):\n",
    "    return 2 * x + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4be95e39",
   "metadata": {},
   "outputs": [],
   "source": [
    "def instructor_name():\n",
    "    return \"Alessia Fitz Gibbon\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62575d10",
   "metadata": {},
   "outputs": [],
   "source": [
    "def square(x):\n",
    "    return x * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d0acbd3a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_grade(points):\n",
    "    grade = points * 10\n",
    "    return grade"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d481695",
   "metadata": {},
   "source": [
    "## How many `x` variables? Which ones?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "51f832f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def square(x):\n",
    "    return x * x\n",
    "\n",
    "def abs(x):\n",
    "  if x < 0:\n",
    "    return -x\n",
    "  else:\n",
    "    return x\n",
    "\n",
    "# main program\n",
    "x = 42\n",
    "sq3 = square(3)\n",
    "sq4 = square(4)\n",
    "print(sq3 + sq4)\n",
    "print(x)\n",
    "x = -22\n",
    "result = abs(x)\n",
    "print(result)"
   ]
  }
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