SOLUTION: Write an equation for a function that is the graph of {{{ y=1/x^3 }}} reflected through the y-axis and shifted down 3 units

Algebra ->  Rational-functions -> SOLUTION: Write an equation for a function that is the graph of {{{ y=1/x^3 }}} reflected through the y-axis and shifted down 3 units      Log On


   

Question 278070: Write an equation for a function that is the graph of +y=1%2Fx%5E3+ reflected through the y-axis and shifted down 3 units
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation for a function that is the graph of y=1%2Fx%5E3 reflected through the y-axis and shifted down 3 units,
We start with the graph of y=1%2Fx%5E3
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C1%2Fx%5E3%29
It has the x and the y-axis as asymptotes
Then we reflect it through the y-axis by replacing x by -x.
y=1%2Fx%5E3 becomes
y=1%2F%28-x%29%5E3
which simplifies to:
y=-1%2Fx%5E3
This gives the graph below
graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C11%2C-1%2Fx%5E3%29
with the same two asymptotes.
Finally we shift it down 3 units by subtracting 3 from the
right side, which gives the equation
y=-1%2Fx%5E3-3}
and the graph is:

The blue dotted line is the asymptote. The original curve had
the x-axis and y-axis as its asymptotes, and this new graph has the line y=-3 as its horizontal asymptote, and has the y-axis as its vertical asymptote..
Edwin