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avatar+2291 

Not sure what the holes are 

RainbowPanda  Nov 14, 2018
 #1
avatar+92785 
+2

29)   factor top / bottom

 

( x + 2) ( x - 2)

___________

-3 ( x + 3)

 

"Holes"  will only be created when we can "cancel" factors

Here....nothing "cancels"  ....so......no "holes"

We will have  a vertical asymptote at x  = -3    and something known as a "slant asymptote"

The latter will occur because we have a greater degree polynomial divided by a lesser degree polynomial

 

 

30)   factor top / bottom

 

(x + 3) ( x - 2)                    (x + 3) ( x - 2)

______________   =       _____________

3 ( x^2 + 4x + 3)               3(x + 3) ( x + 1)

 

 

Note that  the  "x + 3"  factor  will "cancel"

So.....to find the "hole".....set    x +  3  =  0    and solve for x......and we have

 

x + 3  =   0

x  =  -3

 

So.....we have a hole at  x  = -3

 

See the graph, here :  https://www.desmos.com/calculator/oshh1sofob

 

RP.....If you hold down the left button on your mouse/laptop  and drag the cursor along the curve...note....at  x  = -3.....you will see "undefined"   =  (a "hole" here )

 

 

 

cool cool cool

CPhill  Nov 14, 2018
 #2
avatar+2291 
+1

tysm!

RainbowPanda  Nov 14, 2018

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