Question

The graph of the function f(x)=1x+3−15 is a transformation of the graph of the function g(x)=1x by

Answer 1

Given:

The graph of the function

`f(x)=(1)/(x+3)-15`

is a transformation of the graph of

`g(x)=(1)/(x)`

Required:

Find the vertical and the horizontal shift of units.

Step-by-step explanation:

The graph of

`f(x)=(1)/(x+3)`

shift the graph of

`g(x)=(1)/(x)`

left 3 units by subtracting 3 from the x-coordinates of the points on the graph of 1/x.

The graph of

`g(x)=(1)/(x+3)-15`

shift the graph of

`g(x)=(1)/(x+3)`

down 15 units by subtracting 15 from the y-coordinates of the points on the graph of

`g(x)=(1)/(x+3)`

Thus the graph

`f(x)=(1)/(x+3)-15`

shift the graph of

`g(x)=(1)/(x)`

horizontal left 3 units and the vertical shift down 15 units.

Final Answer:

Vertical shift - down 15 units

Horizontal shift - left 3 units