[MATH 121] - Midterm Exam Guide - Ultimate 19 pages long Study Guide!

• School: Queen's University
• Department: Mathematics
• Course: MATH 121
• Professor: Alan Ableson

Document Summary

Goals: to review core function families and mathematical transformations. Below is a graph of: ln(x) 3. 4. (or : y= x= 0, y= 1 x=1, y 2. 7. The red line is: y= ln(x) x=0, y= dne x=1, y= 0. The blue line is ln(x: y= x=0, y=o x=2, y=4. The green line is: y= x= 0, y=0. Don"t necessarily have a lot in common within the family. Functions with 2 or more algebraic terms. Can be remembered by ratio"s because rational functions are ratio"s of polynomial functions as a set of rational functions. When x is negative the y value remains the absolute value of x, which is positive. They are made up of other function families at different intervals of a question. Unit 1: transformation of a functions; exponential and logarithms. Example: transform the graph of y=(cid:2870) into y= 4- (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) y=(cid:2870: y=(cid:2870) y= (cid:4666)+(cid:883)(cid:4667)(cid:2870) The vertical scaling is halved: y= (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870) y= - (cid:2869)(cid:2870)(cid:4666)+(cid:883)(cid:4667)(cid:2870)