Question

the function g(x) was obtained by transforming f(x)=1/xuse the description of the transformation to write the equation representing g(x).f(x) is vertically stretched by a factor of 2,reflected about the x-axis, then shifted left 5 units.

Answer 1

You have the following function:

f(x) = 1/x

In order to determine the shape of g(x), consider each transformation:

- f(x) is vertically stretched by 2

f(x) => 2·f(x) = 2/x

- then, it is reflected about x-axis:

2/x => -2/x

- then, it is shifted left 5 units

-2/x => -2/(x + 5)

Hence, the shape of g(x) is

g(x) = -2/(x + 5)