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Worksheet: Graphs of Rational Functions

In this worksheet, we will practice sketching the graphs of simple rational functions and identify simple rational functions from their graphs.

Q1:

Which of the following graphs represents 𝑓 ( π‘₯ ) = 1 π‘₯ + 1 ?

  • A(a)
  • B(b)
  • C(d)
  • D(c)

Q2:

If a rational function has a horizontal asymptote, then the degree of the numerator is at most the degree of the denominator. Is this true or false?

  • A true
  • B false

Q3:

Consider the following graphs.

Which of these is the graph of 𝑓 ( π‘₯ ) = ( π‘₯ + 1 ) ( π‘₯ βˆ’ 1 ) ( π‘₯ + 3 ) 2 ?

  • A (b)
  • B (a)
  • C (d)
  • D (c)

Q4:

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

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

Q5:

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

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