RATIONAL FUNCTIONS Graphing And Analysis (Page 19 of 19)

The reason for the "hole" is that the rational function is not fully reduced. When written in factored form f(x) = (x(x+3))/((x-1)(x+3)), observe there is a common factor of x + 3. The function can be reduced with the condition that x is not equal to -3: f(x) = x/(x-1), x is not equal to -3.

Now that we have a nice graph, let's conclude by drawing the horizontal and vertical asymptotes. Enter the horizontal asymptote y = 1 as a function Y2, and draw the vertical asymptote at x = 1 using the DRAW Vertical command from the Home screen.

 Y= key. Down arrow key. Down arrow key. 1

 2nd QUIT key. CLEAR key.
 2nd DRAW key. 4: menu selection. 1 ENTER key.

 Calculator screen image. Calculator screen image.
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