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Giải bài 1 trang 17 sách bài tập toán 11 - Chân trời sáng tạo tập 2

Vẽ đồ thị hàm số (y = {left( {sqrt 2 } right)^x}).

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

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Vẽ đồ thị hàm số \(y = {\left( {\sqrt 2 } \right)^x}\).

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về đồ thị hàm số mũ để vẽ đồ thị hàm số \(y = {a^x}\): + Tập xác định: \(\mathbb{R}\). + Xác định sự biến thiên của hàm số. + Lập bảng giá trị của hàm số tại một số điểm. + Xác định các điểm trong bảng trên lên mặt phẳng tọa độ. + Từ đó vẽ được đồ thị hàm số \(y = {a^x}\).

Lời giải chi tiết

Tập xác định: \(\mathbb{R}\). Vì \(\sqrt 2  > 1\) nên hàm số đồng biến trên \(\mathbb{R}\). Bảng giá trị:
x \( - 2\) \( - 1\) 0 1 2
\(y = {\left( {\sqrt 2 } \right)^x}\) \(\frac{1}{2}\) \(\frac{1}{{\sqrt 2 }}\) 1 \(\sqrt 2 \) 2
Đồ thị hàm số \(y = {\left( {\sqrt 2 } \right)^x}\) đi qua các điểm có tọa độ theo bảng giá trị và nằm phía trên trục hoành. Ta vẽ được đồ thị hàm số:

 

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