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Help 9

NotSoSmart  Mar 8, 2018
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2+0 Answers

 #1
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+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
avatar+86528 
+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

 

 

 

cool cool cool

CPhill  Mar 8, 2018

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