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avatar+273 

1. Given the functions f(x)=1/x−3   (to the side of the fraction)  +1      and g(x)=1/x+4     (to the side of the fraction)+3 .

Which statement describes the transformation of the graph of function f onto the graph of function g?

 

Options:

 

The graph shifts 2 units right and 7 units down.

The graph shifts 7 units right and 2 units down.

The graph shifts 2 units left and 7 units up.

The graph shifts 7 units left and 2 units up.

 

2.

What are the coordinates of the hole in the graph of the function f(x) ?

 

f(x)=x^2+3x−28/x+7

 

_____, _______

 

Thanks again. Happy Valentnes day.

 Feb 14, 2019
 #1
avatar+98090 
+2

First one

 

f(x) =   1 / (x - 3) + 1

 

g(x)  = 1 / (x + 4) + 3

 

g(x) is translated 7 units to the left and 2 units up

 

Second one

 

(x^2 + 3x - 28)  / ( x + 7)       factor the numerator

 

[ ( x + 7)   (x - 4) ]  /( x + 7)        cancel the ( x + 7)

 

x - 4

 

Since  x = - 7   makes the denominator of the original fraction = 0.....the "hole" occurs at x = -7

 

To find the y coordinate of the "hole"...put -7 into   x - 4    for x   =  - 7 - 4  =  -11

 

So....the "hole" occurs at  ( -7, -11)

 

 

cool cool  cool

 Feb 14, 2019
 #2
avatar+273 
+1

Thank you so much for your help! As always, your explanations are always easier to understand. :)

PhoenixForever  Feb 14, 2019
 #3
avatar+98090 
0

Thanks, PF.....I try   !!!!

 

 

cool cool cool

CPhill  Feb 14, 2019

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