Functions & Graphs
函數與圖像
A function turns an input into an output. In this lesson you will learn what a function is, how linear functions work, and how to plot their graphs.
函數把輸入變成輸出。在這一課，你會學習甚麼是函數、線性函數如何運作，以及怎樣畫它們的圖像。
1 · What is a function?
甚麼是函數？
A function is a rule that takes an input and gives an output. Think of it as a machine: you put a number in, it does something, and a new number comes out. f(x) = x + 3 means "add 3 to the input".
函數是一條規則：輸入一個數，得出一個輸出。把它想成一部機器：放入一個數，它做某些運算，然後輸出一個新數。f(x) = x + 3 是指「把輸入加 3」。
2 · Linear functions
線性函數
A linear function is a straight-line function, written as y = mx + c. The m is the gradient (how steep the line is), and c is the y-intercept (where the line crosses the y-axis).
線性函數是直線函數，寫作 y = mx + c。m 是斜率（線有多斜），c 是y 截距（線與 y 軸相交的位置）。
3 · Gradient and intercept
斜率與截距
In y = 2x + 1, the gradient is 2 and the y-intercept is 1. The gradient tells you how much y goes up when x goes up by 1.
在 y = 2x + 1 中，斜率是 2，y 截距是 1。斜率告訴你當 x 增加 1 時，y 增加多少。
4 · Plotting graphs
畫圖像
To plot a graph, make a table of x and y values, then plot the points and join them. For y = x + 1: when x = 0, y = 1; when x = 1, y = 2; when x = 2, y = 3.
要畫圖，先做一個 x 和 y 的數值表，然後畫出各點並連線。對於 y = x + 1：當 x = 0，y = 1；當 x = 1，y = 2；當 x = 2，y = 3。
5 · Quick check
小測驗