Domain: All real numbers except x=0 Range: All real numbers except y=0
Practice makes perfect
We want to draw the asymptotes and the graph of the given function. We will start by considering some possible transformations.
Transformations of y= 1x, x≠ 0
Vertical Stretch or Shrink
Vertical stretch, a>1
y=a/x
Vertical shrink, 0< a< 1
y=a/x
Note that if the graph of the function is translated, the asymptotes are also translated in the same distance and direction. Consider the function.
y=4/x
The given function is a combination of transformations.
Vertical stretch by a factor of 4
Let's apply this transformation. We will apply a vertical stretch to the parent function, y= 1x, by a factor of 4.
Now let's look at the graph of the given function and its asymptotes alone.
We can see that the vertical asymtpote is the line x=0, and the equation of the horizontal asymptote is y=0. Using this information, we can state the domain and range of the function.
Domain:& All real numbers except x=0
Range:& All real numbers except y=0
