Graphical Relationships

Sketch the graph of \[ y = \left| \frac{x + 1}{x}\right| \]

Sketch the inner function

The inner function is \[ y = \frac{x + 1}{x} \] To find the intercepts, when y = 0, \[ \begin{align} 1 + \frac{1}{x} &= 0 \\ x &= -1 \end{align} \ \] When x = 0, y is undefined.

Vertical asymptotes is x = 0
When x becomes large (positive or negative), y aproaches 1.
Horizontal asymptote is y = 1. So y looks like:

Reflect negative ordinates of f in the x-axis

The final sketch looks like this:

You will gain most benefit if you work through each problem first and then come back and check your work against the solution.

y

Now You Try:

Sketch the graph of \[ y = \left| \frac{x - 1}{x}\right| \]