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Worksheet: Graphs of Polynomial Functions

In this worksheet, we will practice investigating the graph of polynomial functions and identifying the equation of a polynomial function from its graph and vice versa.

Q1:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 − 2 ) 3 ?

  • A
  • B
  • C
  • D
  • E

Q2:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 − 1 ) ( 𝑥 + 1 ) 2 2 ?

  • A
  • B
  • C
  • D
  • E

Q3:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 − 2 ) ( 𝑥 + 2 ) 2 ?

  • A
  • B
  • C
  • D
  • E

Q4:

Solve 𝑥 − 4 𝑥 + 4 = 0 2 by factoring, and hence determine which of the following figures would be a sketch of 𝑦 = 𝑥 − 4 𝑥 + 4 2 .

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 − 3 ) ( 𝑥 + 1 ) ( 𝑥 + 4 ) ?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 − 3 ) ( 𝑥 + 1 ) ( 𝑥 + 4 ) ?

  • A
  • B
  • C
  • D
  • E

Q7:

The given graph represents a polynomial function.

Which of the following could be the expression 𝑓 ( 𝑥 ) ?

  • A − 2 ( 𝑥 + 1 ) ( 𝑥 − 5 ) ( 𝑥 − 7 ) ( 𝑥 − 9 )
  • B ( 𝑥 + 3 ) ( 𝑥 − 1 ) ( 𝑥 − 2 ) ( 𝑥 − 7 )
  • C 7 ( 𝑥 + 1 ) ( 𝑥 − 5 ) ( 𝑥 − 7 ) ( 𝑥 − 9 )
  • D − 5 ( 𝑥 + 3 ) ( 𝑥 − 1 ) ( 𝑥 − 2 ) ( 𝑥 − 7 )
  • E − 5 ( 𝑥 + 3 ) ( 𝑥 − 1 ) ( 𝑥 − 2 ) ( 𝑥 + 7 )

Q8:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 + 2 ) 3 ?

  • A
  • B
  • C
  • D
  • E

Q9:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 − 2 ) ( 𝑥 + 2 ) 2 ?

  • A
  • B
  • C
  • D
  • E

Q10:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 − 3 ) ( 𝑥 + 1 ) ( 𝑥 + 2 ) ( 𝑥 − 2 ) ?

  • A
  • B
  • C
  • D
  • E

Q11:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 + 2 ) ( 𝑥 − 2 ) 2 ?

  • A
  • B
  • C
  • D
  • E

Q12:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 + 3 ) ( 𝑥 − 1 ) ( 𝑥 − 4 ) ?

  • A
  • B
  • C
  • D
  • E

Q13:

Which of the following is the graph of 𝑓 ( 𝑥 ) = ( 𝑥 + 1 ) ( 𝑥 − 2 ) ( 𝑥 − 1 ) 2 ?

  • A
  • B
  • C
  • D
  • E

Q14:

Which of the following is the graph of 𝑓 ( 𝑥 ) = − ( 𝑥 + 3 ) ( 𝑥 − 1 ) ( 𝑥 + 2 ) ( 𝑥 − 2 ) ?

  • A
  • B