#1**+1 **

Second one

https://es.symbolab.com/solver/functions-calculator/f%5Cleft(x%5Cright)%3D%5Cfrac%7Bx%5E%7B2%7D%2B5x-6%7D%7Bx%5E%7B2%7D-16%7D

Guest Mar 8, 2018

#2**+1 **

Let's do a little detective work.....

x^2 - 16 factors as ( x + 4) ( x - 4) so we have vertical asypmtotes at x = - 4 and x = 4

This rules out the first graph

Note that when x = 0 the y intercept = -6/16 = 3/8 .....this rules out the third graph which has a negative y intercept

Now.....let's find the zeroes of the function (where the grpah intercepts the x axis ) by solving this

x^ 2 + 5x - 6 = 0

(x - 1) ( x + 6) = 0

Setting both of these to 0 and solving produces x = 1 and x = -6

Note that the second graph meets all the criteria

1. Vertical asymptotes at x = -4 and x = 4

2. Positive y intercept

3. Zeroes (roots) at x = -6 and x = 1

CPhill Mar 8, 2018