MAT 1300 Lecture Notes - Lecture 1: Negative Number

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Hung-Chang Liao

Document Summary

A function has an output for every input. Note: an input cannot have two different outputs. This is not a function (input 3 has two different outputs) Example1 f(x)= x2+2: find f(2, solve f(x)=6. Diagram by teacher: find f(4, solve f(x)=2 solution, f(4)=1, [1,2] Cannot take square root of a negative number. Find the domains of : f(x) = sqrt (x-1, g(x) = 3/ 2-x solution, we want x-1 >= 0. So x>= 1 or [1, + infinity: we need 2-x not to equal 0 so x>2 or x<2 (2, +infinity) u (-infinity, 2) X g g(x) f f(g(x)) A linear function is a function of the form f(x)=mx+b. M is the slope ---- if a function grows horizontally by 1 unit it also grows vertically by m units units. Write a formula for the linear function passing through (1,2) and (-2,4) =4-2/-2-1 = -2/3 so f(x) = -2/3 x + b use one of the points using (1,2)