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.

PhoenixForever Feb 14, 2019

#1**+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)

CPhill Feb 14, 2019

#2**+1 **

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

PhoenixForever
Feb 14, 2019