g(x)=3(1/x+1)-2
⇕
g(x)=3(1/x-( -1))+( -2)
We can see that a=3, h= -1, and k= -2. From here, we can determine the transformations.
A vertical stretch by a factor of 3.
A horizontal translation 1 unit to the left.
A vertical translation 2 units down.
Using these transformations, we can find the asymptotes and the reference points of the graph of g(x). Note that the horizontal translation affects only the x-coordinates, while the vertical stretch and vertical translation affect only the y-coordinates.
Object
f(x)=1/x
g(x)=3(1/x-(-1))+(-2)
Vertical asymptote
x=0
x=0+( -1) ⇕ x=- 1
Horizontal asymptote
y=0
y=0+( -2) ⇕ y=- 2
Reference point
(-1,-1)
(-1+( -1),3(- 1)+( -2)) ⇕ (-2,-5)
Reference point
(1,1)
(1+( -1),3(1)+( -2)) ⇕ (0,1)
Next, we will use the table above to graph f(x) and g(x).
Finally, we will state the domain and range of g(x). Since x=-1 is the vertical asymptote and y=-2 is the horizontal asymptote, we will exclude them from the domain and range, respectively.
