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# Help 9 ​

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Help 9     Mar 8, 2018

### 2+0 Answers

#1
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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

Mar 8, 2018
#2
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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   Mar 8, 2018