LOGARITHMIC FUNCTIONS AND ITS GRAPH || GRADE 11GENERAL MATHEMATICS Q1

Summary

Key Points

• Key properties of basic logarithmic functions include being a one-to-one function, having an x-intercept at (1,0), no y-intercept, and a vertical asymptote at x=0. 0:26
• The domain of a logarithmic function in the form y = log_b(f(x)) is determined by setting the argument f(x) strictly greater than zero (f(x) > 0) and solving for x. 0:26
• Logarithmic functions are characterized by a domain of all positive numbers (x > 0) and a range of all real numbers. 0:39
• To graph a logarithmic function, one must construct a table of values by substituting x-values and calculating corresponding y-values, then plot these points and connect them with a smooth curve. 1:27
• The vertical asymptote of a logarithmic function y = log_b(f(x)) is found by setting the argument f(x) equal to zero (f(x) = 0) and solving for x. 12:08
• To find the x-intercept, set the function's output y equal to zero and solve the resulting logarithmic equation for x, often by converting it to exponential form. 13:15
• The range of any logarithmic function is consistently the set of all real numbers, spanning from negative infinity to positive infinity. 19:00
• To find the y-intercept, set the input x equal to zero and solve for y; if this results in a non-positive argument for the logarithm, then no y-intercept exists. 19:27
• The zeros of a logarithmic function are the x-values where the function crosses the x-axis, which are precisely the x-coordinates of the x-intercepts. 19:27