## 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=b^{2} - 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, (x_{1}, y_{1}), then y-y_{1} = m(x-x_{1})
iv) h(t) = -16 t^{2} + v_{0}t + h_{0}