Do a rough sketch of the graphs of the following rational functions by finding (1) the vertical asymptote, (2) the horizontal asymptote, and (3) selecting a number of representative points and graphing, as was suggested in Section 3.6.

(1) Setting the denominator equal to zero and solving for x to find the vertical asymptote,

(2) Solving the original equation for x to find the horizontal asymptote,

Then setting the denominator equal to zero and solving for y,

(3) Finding representative points and graphing in Fig. 3-19,

(1) Vertical asymptote: x = 4 (2) Multiplying both sides of the equation by (x – 4) and solving for x to find the horizontal asymptote,

Then setting the denominator equal to zero and solving for y,

For step (3), see top of next page.

Transcribed Image Text:

+ y -7-6-5-4-3-2-1 -2 3+ y= x + 8x+12 (-4-4) 5 +x 1 2