Worksheet: Equation of a Polynomial from a Sketch

In this worksheet, we will practice identifying a polynomial function from a sketch of its graph.

Q1:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 1 ) ( 𝑥 + 3 ) ( 𝑥 3 )
  • B 𝑦 = ( 𝑥 + 1 ) ( 𝑥 + 3 ) ( 𝑥 3 )
  • C 𝑦 = ( 𝑥 1 ) ( 𝑥 + 3 ) ( 𝑥 3 )
  • D 𝑦 = ( 𝑥 + 1 ) ( 𝑥 + 3 ) ( 𝑥 3 )
  • E 𝑦 = 𝑥 ( 𝑥 + 1 ) ( 𝑥 + 3 )

Q2:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 2 ) ( 𝑥 + 5 )
  • B 𝑦 = ( 𝑥 + 2 ) ( 𝑥 5 )
  • C 𝑦 = ( 𝑥 2 ) ( 𝑥 + 5 )
  • D 𝑦 = ( 𝑥 + 2 ) ( 𝑥 5 )
  • E 𝑦 = ( 𝑥 + 2 ) ( 𝑥 + 5 )

Q3:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 7 ) 3
  • B 𝑦 = ( 𝑥 + 7 ) 3
  • C 𝑦 = ( 𝑥 + 7 ) 3
  • D 𝑦 = ( 𝑥 7 ) 3
  • E 𝑦 = 𝑥 + 7 3

Q4:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = 𝑥 ( 𝑥 5 ) ( 𝑥 + 6 )
  • B 𝑦 = 𝑥 ( 𝑥 5 ) ( 𝑥 + 6 )
  • C 𝑦 = 𝑥 ( 𝑥 + 5 ) ( 𝑥 6 )
  • D 𝑦 = 𝑥 ( 𝑥 + 5 ) ( 𝑥 6 )
  • E 𝑦 = 𝑥 ( 𝑥 + 5 ) ( 𝑥 + 6 )

Q5:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 + 7 ) ( 𝑥 + 1 ) 2
  • B 𝑦 = ( 𝑥 + 7 ) ( 𝑥 + 1 ) 2
  • C 𝑦 = ( 𝑥 1 ) ( 𝑥 7 ) 2
  • D 𝑦 = ( 𝑥 7 ) ( 𝑥 1 ) 2
  • E 𝑦 = ( 𝑥 + 1 ) ( 𝑥 + 7 ) 2

Q6:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 4 ) ( 𝑥 + 4 ) 2
  • B 𝑦 = ( 𝑥 + 4 ) ( 𝑥 4 ) 2
  • C 𝑦 = ( 𝑥 4 ) ( 𝑥 + 4 ) 2
  • D 𝑦 = ( 𝑥 + 4 ) ( 𝑥 4 ) 2
  • E 𝑦 = 𝑥 ( 𝑥 + 4 ) ( 𝑥 4 )

Q7:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 + 7 ) ( 𝑥 + 2 ) ( 𝑥 2 ) ( 𝑥 8 )
  • B 𝑦 = ( 𝑥 + 7 ) ( 𝑥 + 2 ) ( 𝑥 2 ) ( 𝑥 8 )
  • C 𝑦 = ( 𝑥 7 ) ( 𝑥 + 2 ) ( 𝑥 2 ) ( 𝑥 + 8 )
  • D 𝑦 = ( 𝑥 7 ) ( 𝑥 + 2 ) ( 𝑥 2 ) ( 𝑥 + 8 )
  • E 𝑦 = ( 𝑥 7 ) ( 𝑥 + 2 ) ( 𝑥 2 ) ( 𝑥 8 )

Q8:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 2 ) ( 𝑥 + 4 )
  • B 𝑦 = ( 𝑥 2 ) ( 𝑥 + 4 )
  • C 𝑦 = ( 𝑥 + 2 ) ( 𝑥 4 )
  • D 𝑦 = ( 𝑥 + 2 ) ( 𝑥 4 )
  • E 𝑦 = ( 𝑥 2 ) ( 𝑥 4 )

Q9:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 + 2 ) ( 𝑥 3 ) ( 𝑥 5 )
  • B 𝑦 = ( 𝑥 2 ) ( 𝑥 + 3 ) ( 𝑥 + 5 )
  • C 𝑦 = ( 𝑥 + 2 ) ( 𝑥 3 ) ( 𝑥 5 )
  • D 𝑦 = ( 𝑥 2 ) ( 𝑥 + 3 ) ( 𝑥 + 5 )
  • E 𝑦 = ( 𝑥 2 ) ( 𝑥 3 ) ( 𝑥 5 )

Q10:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 5 ) ( 𝑥 + 4 ) 2 2
  • B 𝑦 = ( 𝑥 + 5 ) ( 𝑥 4 ) 2 2
  • C 𝑦 = ( 𝑥 5 ) ( 𝑥 + 4 ) 2 2
  • D 𝑦 = ( 𝑥 + 5 ) ( 𝑥 4 ) 2 2
  • E 𝑦 = ( 𝑥 5 ) ( 𝑥 4 ) 2 2

Q11:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 + 2 ) ( 𝑥 + 2 ) 2 2
  • B 𝑦 = ( 𝑥 + 2 ) ( 𝑥 2 ) 2 2
  • C 𝑦 = ( 𝑥 2 ) ( 𝑥 2 ) 2 2
  • D 𝑦 = ( 𝑥 + 2 ) ( 𝑥 2 ) 2 2
  • E 𝑦 = ( 𝑥 + 2 ) ( 𝑥 + 2 ) 2 2

Q12:

Which of the following functions is graphed in the given figure?

  • A 𝑦 = ( 𝑥 + 5 ) ( 𝑥 5 ) 3
  • B 𝑦 = ( 𝑥 5 ) ( 𝑥 + 5 ) 3
  • C 𝑦 = ( 𝑥 5 ) ( 𝑥 + 5 ) 3
  • D 𝑦 = ( 𝑥 + 5 ) ( 𝑥 5 ) 3
  • E 𝑦 = ( 𝑥 + 5 ) ( 𝑥 5 ) 3 2

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