Approaching Graphing Rational Expressions

If the degree of the numerator is equal to the degree of the denominator,

• there is no horizontal asymptote.

• the horizontal asmptote is the y axis.

• the horizontal azymptote is the lead coefficient of the numerator over the lead coefficient of the denomiator

• The horizontal asymptote is y = 0

If the degree of the numerator is greater than the degree of the denominator,

• there is no horizontal asymptote.

• the horizontal asmptote is the y axis.

• the horizontal azymptote is the lead coefficient of the numerator over the lead coefficient of the denomiator

• The horizontal asymptote is y = 0

When graphing rational expressions, you can determine the ​ (a)   asymptote by setting the ​ (b)   equal to zero and solving.

• vertical
• denominator
• horizontal
• numerator
• expression

When graphing rational expressions, the x-intercepts can be determined by setting the ​ ​ (a)   ​ equal to zero and solving.

• numerator
• denominator
• expression
• variable

If the degree of the numerator is less than the degree of the denominator,

• there is no horizontal asymptote.

• the horizontal asmptote is the y axis.

• the horizontal azymptote is the lead coefficient of the numerator over the lead coefficient of the denomiator

• The horizontal asymptote is y = 0

The steps to graphing a rational expression, in order, are:

• Simplify the expression

• Find the x-intercepts

• Determine the vertical asymptotes

• Determine the horizontal asymptote

• Identify any holes in the graph.

Simplify:  (x²+11x+24)/(x²+4x-32)

• A.(x+7)/(x+4)

• B.3/4

• C.(x+3)/(x+4)

• D.(x+3)/(x-4)

Simplify.

• A

• B

• C

• D

• (-2, 0)

• (0,-2)

• (2,0)

• (0,2)

• There is no hole.

Graph the horizontal asymptote of the expression (x²+11x+24)/(x²+4x-32).