Use your calculator to find the values of the following: a 91 b 1 91 c 62 d 1 62 e 34 f

Weird R Graphs of functions in R² are curves Set of infinite points {(x,y) such that y=f(x) Graphs of functions in R³ are surfaces z=f(x,y) {(x,y) such that z=f(x,y) Test 1 Review Log, hn- solving, inverses, evaluating average velocity Rational fins- holes vs VA domains of f*g Sign analysis Solve 1. find roots of all factors Sign chart Graph (-3,0]U{2} 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) e=2.71828ish E in mma Log[] in mma is natural log log base ten is Log[10,x] just use log log3(1/81) = -4 ln(1)=0 log2(256) = 8 ln(e)=1 ln(e)=1 Logs (solving) ln(ln(x)=-1.4 e^(ln(ln(x)))=e^-1.4 ln(x)=e^-1.4 e^(ln(x))=e^e^-1.4 x=e^e^-1.4 9^x=e^(x+5) ln(9^x)=(ln(e^(x+5))) xln(9)=x+5 xln(9)-x=5 x(ln(9)-1)=5 x=5/(ln(9)-1) try to write ln with parentheses Logs (inverses) 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 0=y^2 -2y-ln(x) y=(2+-sqrt(4+4ln(x))/2 Range(f^-1)=Dom(f)=(-∞,1) x=1 f^(-1)=(2+sqrt(4+0))/2 or e^(y^2 -2y) ==:y or InverseFunction[x] Example f(x)=((x+4)(x-3)(x+3))/((x+4)(x-3)^2) 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 funcbefore simplifying 1. If at least one copy of (x-a) remains in the denominaafter simplifying, we have