SOLUTION: Given the function f(x)=1/x , write the equation g(x) after the following transformations: horizontal stretch by the factor 2, vertical stretch by the factor 5 reflection in the

Algebra ->  Rational-functions -> SOLUTION: Given the function f(x)=1/x , write the equation g(x) after the following transformations: horizontal stretch by the factor 2, vertical stretch by the factor 5 reflection in the      Log On


   

Question 1165859: Given the function f(x)=1/x , write the equation g(x) after the following transformations:
horizontal stretch by the factor 2,
vertical stretch by the factor 5
reflection in the y-axis
translation 1 unit left and 3 units down
Determine the domain and range of the transformed function.
Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
We begin with 

y=1%2Fx
horizontal stretch by the factor 2,

We replace x by x/2

y=1%5E%22%22%2F%28x%2F2%29
which simplifies to
y=2%2Fx
vertical stretch by the factor 5

We multiply the whole right side by 5

y=10%2Fx
reflection in the y-axis

We replace x by -x

y=10%2F%28-x%29

which simplifies to

y=-10%2Fx
translation 1 unit left
 

We replace x by (x+1)

y=-10%2F%28x%2B1%29
and 3 units down

We subtract 3 from the whole right side:

y=-10%2F%28x%2B1%29-3

get LCD

y+=+-10%2F%28x%2B1%29-3%28x%2B1%29%2F%28x%2B1%29

y+=+%28-10-3%28x%2B1%29%29%2F%28x%2B1%29

y+=++%28-10-3x-3%29%2F%28x%2B1%29

y+=+%28-3x-13%29%2F%28x%2B1%29

So the answer is

%22g%28x%29%22+=+%28-3x-13%29%2F%28x%2B1%29

Edwin