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Lesson: Graphs of Rational Functions

Worksheet • 5 Questions

Q1:

Which of the following is the equation of the rational function graphed below?

  • A 𝑦 = π‘₯ βˆ’ 2 π‘₯ 2 π‘₯ βˆ’ 1 0  
  • B 𝑦 = π‘₯ βˆ’ 2 π‘₯ 2 π‘₯ βˆ’ 1 0 
  • C 𝑦 = π‘₯ βˆ’ 2 π‘₯ 2 π‘₯ βˆ’ 1 0 οŠͺ  
  • D 𝑦 = π‘₯ βˆ’ 2 π‘₯ βˆ’ 4 2 π‘₯ βˆ’ 1 0 π‘₯  

Q2:

The graph shows 𝑦 = π‘˜ ( π‘₯ βˆ’ π‘Ž ) + 𝑏 . A single point is marked on the graph. What are the values of the constants π‘Ž , 𝑏 , and π‘˜ ?

  • A π‘Ž = 3 , 𝑏 = βˆ’ 2 , π‘˜ = 3
  • B π‘Ž = 4 , 𝑏 = βˆ’ 3 , π‘˜ = βˆ’ 1
  • C π‘Ž = 5 , 𝑏 = 1 , π‘˜ = 4
  • D π‘Ž = βˆ’ 2 , 𝑏 = 3 , π‘˜ = βˆ’ 1 2
  • E π‘Ž = βˆ’ 3 , 𝑏 = 3 , π‘˜ = βˆ’ 1

Q3:

Which of the following is the equation of the rational function graphed below?

  • A 𝑦 = π‘₯ βˆ’ 3 π‘₯ βˆ’ 2 π‘₯ βˆ’ 4 2 2
  • B 𝑦 = π‘₯ βˆ’ 3 π‘₯ βˆ’ 2 π‘₯ βˆ’ 4 3 2
  • C 𝑦 = π‘₯ βˆ’ 2 π‘₯ βˆ’ 3 π‘₯ + 4 2 2
  • D 𝑦 = π‘₯ + 3 π‘₯ π‘₯ + 4 2 2

Q4:

Shown is the graph of the rational function 6 𝑃 ( π‘₯ ) .

Which of the following could be the polynomial 𝑃 ( π‘₯ ) ?

  • A ( π‘₯ βˆ’ 1 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 3 )
  • B ( π‘₯ βˆ’ 1 ) ( π‘₯ + 6 )
  • C ( π‘₯ + 1 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 3 )
  • D ( π‘₯ βˆ’ 1 ) ( π‘₯ βˆ’ 2 ) ( π‘₯ βˆ’ 3 )
  • E βˆ’ ( π‘₯ βˆ’ 1 ) ( π‘₯ + 2 ) ( π‘₯ βˆ’ 3 )

Q5:

Sketch a graph of the equation 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 3 π‘₯ βˆ’ 2 π‘₯ βˆ’ 4 2 2 and determine which graph represents this function.

  • A
  • B
  • C
  • D
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