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Lý thuyết Hàm số mũ. Hàm số lôgarit - Toán 11 Chân trời sáng tạo

1. Hàm số mũ - Hàm số \(y = {a^x}\left( {a > 0,a \ne 1} \right)\) được gọi là hàm số mũ cơ số a.

﷽Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
Quảng cáo

1. Hàm số mũ

- Hàm số \(y = {a^x}\left( {a > 0,a \ne 1} \right)\) được gọi là hàm số mũ cơ số a.

- Hàm số \(y = {a^x}\left( {a > 0,a \ne 1} \right)\) có:+ Tập xác định: \(D = \mathbb{R}\).+ Tập giá trị: \(T = \left( {0; + \infty } \right)\).+ Hàm số liên tục trên \(\mathbb{R}\).+ Sự biến thiên:
  • Nếu a > 1 thì hàm số đồng biến trên \(\mathbb{R}\) và \(\mathop {\lim }\limits_{x \to  + \infty } y =  + \infty ;\mathop {\lim }\limits_{x \to  - \infty } y = 0\).
  • Nếu 0 < a < 1 thì hàm số nghịch biến trên \(\mathbb{R}\) và \(\mathop {\lim }\limits_{x \to  + \infty } y = 0;\mathop {\lim }\limits_{x \to  - \infty } y =  + \infty \).
+ Đồ thị:
  • Cắt trục tung tại điểm (0; 1), đi qua điểm (1; a).
  • Nằm phía trên trục hoành.

2. Hàm số lôgarit

- Hàm số \(y = {\log _a}x\left( {a > 0;a \ne 1} \right)\) được gọi là hàm số lôgarit cơ số a.

- Hàm số \(y = {\log _a}x\left( {a > 0;a \ne 1} \right)\) có:+ Tập xác định: \(D = \left( {0; + \infty } \right)\).+ Tập giá trị: \(T = \mathbb{R}\).+ Hàm số liên tục trên \(\left( {0; + \infty } \right)\).+ Sự biến thiên:
  • Nếu a > 1 thì hàm số đồng biến trên \(\left( {0; + \infty } \right)\) và \(\mathop {\lim }\limits_{x \to  + \infty } y =  + \infty ;\mathop {\lim }\limits_{x \to {0^ + }} y = 0\).
  • Nếu 0 < a < 1 thì hàm số nghịch biến trên \(\left( {0; + \infty } \right)\) và \(\mathop {\lim }\limits_{x \to  + \infty } y =  - \infty ;\mathop {\lim }\limits_{x \to {0^ + }} y =  + \infty \).
+ Đồ thị:
  • Cắt trục hoành tại điểm (1; 0), đi qua điểm (a; 1).
  • Nằm phía phải trục tung.

Quảng cáo

Tham Gia Group Dành Cho Lớp 11 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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