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Worksheet: Sketching 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 + 2 ) 3 ?

  • A
  • B
  • C
  • D
  • E

Q3:

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

  • A
  • B
  • C
  • D
  • E

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

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

  • A
  • B
  • C
  • D
  • E

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

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 )

Q10:

In (a), the graphs of 𝑓 ( 𝑥 ) = ( 𝑥 + 1 ) ( 𝑥 − 2 ) , 𝑔 ( 𝑥 ) = − 2 5 ( 𝑥 − 4 ) , and their product 𝑃 ( 𝑥 ) = − 2 5 ( 𝑥 + 1 ) ( 𝑥 − 2 ) ( 𝑥 − 4 ) are represented. What is the function ℎ if (b) is the graph 𝑦 = ℎ ( 𝑥 ) 𝑃 ( 𝑥 ) ?

  • A ℎ ( 𝑥 ) = 𝑥 − 1 2
  • B ℎ ( 𝑥 ) = 𝑥 − 1
  • C ℎ ( 𝑥 ) = 1 − 𝑥 2
  • D ℎ ( 𝑥 ) = 1 − 𝑥
  • E ℎ ( 𝑥 ) = − 𝑥 − 1 2

Q11:

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

  • 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 − 3 ) ( 𝑥 + 1 ) ( 𝑥 + 2 ) ( 𝑥 − 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