Rationals Answers

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Rationals Answers: Problem 1 :: Problem 2 :: Problem 3

PROBLEM 1: (top)

Graph of :

Features of the Graph:

• End behavior towards horizontal asymptote at y=1/3.
• Root at x=2; passes through the axis
• Vertical asymptote at x=-2/3; opposite behavior around asymptote
• Vertical asymptote at x=0; opposite behavior around asymptote
• Vertical asymptote at x=1; opposite behavior around asymptote

 

 

 

PROBLEM 2: (top)

Graph of :

Features of the Graph:

• End-behavior:
• Root at x=1; passes through the axis
• Root at x=5; bounces off the axis
• Point discontinuity at x=-1 (results from factoring out (x-1) from numerator and denominator)
• Vertical asymptote at x=-2 with opposite behavior approaching the asymptote.

 

 

 

 

 

PROBLEM 3: (top)

Graph of :

Features of the Graph:

• End-behavior towards 0 in both directions
• Root at x=3; passes through the axis
• Root at x=-3; bounces off the axis (note that the graph is growing as it approaches -3 from the right, hits 0 at x=-3, decreases briefly, then grows again towards, but never reaching, the x-axis. This behavior will become clearer with study of calculus)
• Vertical asymptote at x=0; identical behavior around asymptote (approaches -infinity from both sides)
  

 

 

This page last updated 19 June, 2008 4:30 PM