Logarithmic Function and its Graph — الرياضيات البحتة الصف الثاني الثانوي لغات

درس «Logarithmic Function and its Graph» فى مادة الرياضيات البحتة لـالصف الثاني الثانوي لغات من وحدة «Unit 2: Exponents, Logarithms and Their Applications». This lesson introduces the logarithmic function as the inverse of the exponential function, defining y = log_a(x) iff a^y = x, analyzing its domain R+ and range R, and graphing curves for a > 1 and 0 < a < 1. هتتعلم فى الدرس ده: The logarithmic function f(x) = log_a(x) is the inverse of the exponential function y = a^x (a > 0, a != 1).، Domain is R+ (]0, ∞[), range is R, and the graph passes through the fixed point (1, 0).، If a > 1, f(x) = log_a(x) is strictly increasing on ]0, ∞[.، If 0 < a < 1, f(x) = log_a(x) is strictly...

الدرس ده من وحدة «Unit 2: Exponents, Logarithms and Their Applications» فى مادة الرياضيات البحتة لـالصف الثاني الثانوي لغات على منصة دروسات.

الدرس متاح بالاشتراك: ترم كامل أو المادة لوحدها.

ملخص الدرس

This lesson introduces the logarithmic function as the inverse of the exponential function, defining y = log_a(x) iff a^y = x, analyzing its domain R+ and range R, and graphing curves for a > 1 and 0 < a < 1.

هتتعلم إيه فى الدرس ده

• The logarithmic function f(x) = log_a(x) is the inverse of the exponential function y = a^x (a > 0, a != 1).
• Domain is R+ (]0, ∞[), range is R, and the graph passes through the fixed point (1, 0).
• If a > 1, f(x) = log_a(x) is strictly increasing on ]0, ∞[.
• If 0 < a < 1, f(x) = log_a(x) is strictly decreasing on ]0, ∞[.
• The y-axis (x = 0) is a vertical asymptote for the logarithmic curve.