Sharp EL9900 manual Graphing Rational Functions

EL-9900 Graphing Calculator

Graphing Rational Functions

A rational function f (x) is defined as the quotient p (x) where p (x) and q (x) are two q (x)

polynomial functions such that q (x) ≠ 0. The domain of any rational function consists of all values of x such that the denominator q (x) is not zero.

A rational function consists of branches separated by vertical asymptotes, and the values of x that make the denominator q (x) = 0 but do not make the numerator p (x) = 0 are where the vertical asymptotes occur. It also has horizontal asymptotes, lines of the form y = k (k, a constant) such that the function gets arbitrarily close to, but does not cross, the horizontal asymptote when x is large.

The x intercepts of a rational function f (x), if there are any, occur at the x-values that make the numerator p (x), but not the denominator q (x), zero. The y-intercept occurs at f (0).

Example

Graph the rational function and check several points as indicated below.

1.Graph f (x) = x2-1 .

x-1

2.Find the domain of f (x), and the vertical asymptote of f (x).

3.Find the x- and y-intercepts of f (x).

4.Estimate the horizontal asymptote of f (x).

	Before	There may be differences in the results of calculations and graph plotting depending on the setting.
Starting		Return all settings to the default value and delete all data.
		Set the zoom to the decimal window:	ZOOM	A	(	ENTER	ALPHA	) 7
	Step & Key Operation			Display				Notes

1-1Enter y = x - 1 for Y1. x 2 -1

Y=

a/b X//T/n — 1

— 1

1-2View the graph.

GRAPH

X//T/n x2

The function consists of two branches separated by the verti- cal asymptote.

11-1