MAC 1147H Daily Notes

August 23rd
Defined a function as well as mentioned the definition of the domain, range, and co-domain of a function. interval notation [a,b]={x\in R | a≤x≤b} (a,b) = {x\in R| a < x < b} (a,∞) = {x\in R| a< x} Talked about graphing functions. Translating functions and shifts: f(x-k), f(x)+k Absolute value of a function, quadratic functions and Q.F. and discriminant D=b2 - 4ac, as well as the vertex =-b/2a. standard form of a poylnomial. a) If D > 0, then there are two distinct real solutions. b) If D < 0, then there are no real solutions. c) If D = 0, then there is exactly one solution. parabolic form q(x)=a(x-h)2 +k with vertex (h,k) the composition of two functions: (fog)(x)=f(g(x)) the identity function f(x)=x and thenfinding an inverse to function f(x)=y: change x and y then solver for y. read more on 1.7.

August 21st
First day of class. I emphasized that students need to get exact answers and get comfortable with square roots. Lots of memorization; numeracy. We went over i) the distance formula and how it comes from the Pythagorean Theorem. (Page 168.) ii) slope-intercept form of a line: y=mx+b; and vertical lines are of the form x=k iii) point-slope form: gien m, (x1, y1), then y-y1 = m(x-x1) iv) h(t) = -16 t2 + v0t + h0