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

$f(x)=\frac{1}{x+3}-15$

is a transformation of the graph of

$g(x)=\frac{1}{x}$

Required:

Find the vertical and the horizontal shift of units.

Explanation:

The graph of

$f(x)=\frac{1}{x+3}$

shift the graph of

$g(x)=\frac{1}{x}$

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

The graph of

$g(x)=\frac{1}{x+3}-15$

shift the graph of

$g(x)=\frac{1}{x+3}$

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

$g(x)=\frac{1}{x+3}$

Thus the graph

$f(x)=\frac{1}{x+3}-15$

shift the graph of

$g(x)=\frac{1}{x}$

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

Final Answer:

Vertical shift - down 15 units

Horizontal shift - left 3 units