MATH 1271 Study Guide - Midterm Guide: Asymptote, Binary Logarithm, Inverse Function
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Rational fins- holes vs va domains of f*g. Or find roots, and use graphing to solve. Logs (evaluating) logb(x) is defined as the inverse function of b^x ln(x)=loge(x) log log base ten is log[10,x] e=2. 71828ish. E in mma log[] in mma is natural just use ?log log3(1/81) = -4 ln(1)=0 log2(256) = 8 ln(e)=1. Logs (inverses) try to write ln with parentheses f(x)=e^(x^2 -2x) find an inverse f^-1 for f (restricting domain if necessary) Plot f(x)=e^(x^2 -2x), x<= 1 y=e^(x^2 -2x) x=e^(y^2 -2y) ln(x)=ln(e^(y^2 -2y) ln(x)=y^2 -2y quadratic formula. Dom(f) {x=-4,x=3} x cannot equal -4 or 3 (x+3)/(x-3) simplify. Suppose (x-r) is a factor in the denominator of a rational function before simplifying. If at least one copy of (x-a) remains in the denominator after simplifying, we have a vertical asymptote at x=a. If all copies of (x-a) are gone from the denominator after simplifying, then f has a hole at x=a.
