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

Vẽ đồ thị hàm số (y = {log _{frac{3}{2}}}x).

ꦦTổng 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 \(y = {\log _{\frac{3}{2}}}x\).

Phương pháp giải - Xem chi tiết

Sử dụng kiến thức về đồ thị hàm số lôgarit để vẽ đồ thị hàm số \(y = {\log _a}x\): + Tập xác định: \(\left( {0; + \infty } \right)\). + 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 \(y = {\log _a}x\).

Lời giải chi tiết

Tập xác định: \(\left( {0; + \infty } \right)\). Vì \(\frac{3}{2} > 1\) nên hàm số đồng biến trên \(\left( {0; + \infty } \right)\). Bảng giá trị:
x \(\frac{8}{{27}}\) \(\frac{2}{3}\) 1 3 4
\(y\) \( - 3\) \( - 1\) 0 \({\log _{\frac{3}{2}}}3\) \({\log _{\frac{3}{2}}}4\)
Đồ thị hàm số \(y = {\log _{\frac{3}{2}}}x\) đi qua các điểm có tọa độ theo bảng giá trị và nằm bên phải trục tung. Ta vẽ được đồ thị hàm số:

 

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