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Lý thuyết Hàm số bậc nhất y = ax + b (a ≠ 0) SGK Toán 8 - Chân trời sáng tạo

Hàm số bậc nhất là gì?

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1. Hàm số bậc nhất

Khái niệm:

Hàm số bậc nhất🍌 là hàm số được cho bởi công thức y = ax + b với a, b là các số cho trước và a khác 0.

Ví dụ: y = 2x – 3 là hàm số bậc nhất với a = 2 và b = -3y = x + 4 là hàm số bậc nhất với a = 1, b = 4

2. Bảng giá trị của hàm số bậc nhất

Để lập bảng giá trị của hàm số bậc nhất y = ax + b ta lần lượt cho x nhận các giá trị x1; x2; x3; ... (x1; x2; x3๊; ... tăng dần) và tính các giá trị tương ứng của y rồi ghi vào bảng có dạng như sau:

x

x1

x2

x3

...
y = ax + b

y1

y2

y3

...

Chú ý: ღTrong bảng giá trị của hàm số bậc nhất y = ax + b, khi giá trị của x tăng dần:

- Nếu a > 0 thì giá trị của y tăng dần.- Nếu a < 0 thì giá trị của y giảm dần.Ví dụ: Bảng giá trị của hàm số bậc nhất y = f(x) = 5x + 3 với x lần lượt bằng -2; -1; 0; 1; 2 là:
x -2 -1 0 1 2
y = ax + b -7 -2 3 8 13

 3. Vẽ đồ thị của hàm số bậc nhất

Hàm số y = ax (a\( \ne \)0, b = 0)

Đồ thị của hàm số y = ax (a\( \ne \)0)  là một đường thẳng đi qua gốc tọa độ O(0;0).

Cách vẽ:

Bước 1.🧜 Xác định một điểm M trên đồ thị khác gốc tọa độ O, chẳng hạn M(1; a)

Bước 2. Vẽ đường thẳng đi qua hai điểm O và M.

Chú ý: Đồ thị của hàm số y = ax còn được gọi là đường thẳng y = ax.

Ví dụ: Cho hàm số y = 3x.Cho x = 1 ta có y = 3. Ta vẽ điểm A(1; 3)Đồ thị hàm số y = 3x là đường thẳng đi qua các điểm O(0; 0) và A(1; 3)

Hàm số y = ax + b (a\( \ne \)0, b\( \ne \)0)

Đồ thị của hàm số y = ax + b (a\( \ne \)0, b\( \ne \)0) là một đường thẳng:

- Cắt trục tung tại điểm có tung độ bằng b;

- Song song với đường thẳng y = ax.

Cách vẽ:

Bước 1.🔥 Cho x = 0 thì y = b, ta được điểm M(0; b) trên Oy.

Cho y = 0 thì x = \( - \frac{b}{a}\), ta được điểm N(\( - \frac{b}{a}\); 0) trên Ox.

Bước 2.𒆙 Vẽ đường thẳng đi qua hai điểm M và N, ta được đồ thị của hàm số y = ax + b

Chú ý: Đồ thị của hàm số y = ax + b còn gọi là đường thẳng y = ax + b.

Ví dụ: Cho hàm số y = -2x + 4Cho x = 0 thì y =  4, ta được điểm P(0;4)Với y = 0 thì x = 2, ta được điểm Q(2;0)Đồ thị hàm số y = -2x + 4 là đường thẳng đi qua hai điểm P(0;4) và Q(2;0)

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