Control-drag (or type) $p$.

Context Panel: Assign to a Name≻$p$ 

Control-drag (or type) $q$.

Context Panel: Assign to a Name≻$q$ 

Expression palette: Limit operator

Context Panel: Evaluate and Display Inline

Code for Figure 1.5.3(a) is hidden in the cell containing the graph.

To obtain Figure 1.5.3(a) interactively, write the sequence $\frac{p}{q}\,\frac{4}{7}$ and  invoke the Plot Builder from the Context Panel.

The line $y\=4\/7$ is a horizontal asymptote.

Divide $p$ by $x^3$, where 3 is the highest power in the denominator.
Press the Enter key.

Context Panel: Expand≻Expand

Context Panel: Assign to a Name≻$P$ 

Expression palette: Limit operator

Context Panel: Evaluate and Display Inline

Divide $q$ by $x^3$, where 3 is the highest power in the denominator.
Press the Enter key.

Context Panel: Expand≻Expand

Context Panel: Assign to a Name≻$P$ 

Expression palette: Limit operator

Context Panel: Evaluate and Display Inline

Divide $P$ by $Q$

Context Panel: Evaluate and Display Inline

The limit of the rational function $\frac{p}{q}$ is the limit of $\frac{P}{Q}$. Since $\underset{x\to -\infty }{lim}Q\ne 0$, apply the Quotient rule.