Comparing+Functions+by+Meghan+Kean,+Jackie+Kennedy,+and+Monica+Bakhri

Comparing Functions

1. Two Functions: 6/x=y and x-5=y

2. One of the functions does not have a domain that is not all real numbers which is 6/x=y. It has a domain of all real numbers __except 0__ because the x value never passes 0 and is always less than or greater than 0 but never equal to zero. Also the functions intersect at two points, which meets the requirement of one point. We know this because if you set both equations equal to each other and then solve them you can find the spots of intersections.

3. Inequality: 6/x > x-5

4.

5. 6/x = x-5 (6/x)x=(2x-5)x 6=x^2-5x 6-6=x^2-5x-6 0=x^2-5x-6 0=(x-6)(x+1) x=6 and x= -1 (6,0) (-1,0)

The two intersection points are (-1, -6) and (6, 1).

6/x = x-5 6/-1 = (-1)-5 -6 = -6

(-1, -6)

6/x = x-5 6/6 = 6-5 1 = 1

(6, 1)

6. x<-1 or 0we multiplied both sides by x and then subtracted zero from both sides until one side was equal to zero. Then we factored the quadratic equation so we got the x-intercepts, which are 6 and -1. The x-intercepts are also the intersection points because when you plug in 6 for 6/x and x-5 you get the same answers, 6/-1= -6 and (-1)-5= -6 and 6/6=1 and 6-5= 1. When x<-1, 6/x is greater than x-5. This statement can be proved true because if you plug in -6 for x in both equations then 6/-6 is equal to -1 and -6-5 is equal to -11, which proves that when x<-1, 6/x > x-5. When 0 > x-5.