Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.
Start Practicing

Worksheet: Sketching Graphs of Polynomial Functions

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 if (b) is the graph 𝑦 = ( 𝑥 ) 𝑃 ( 𝑥 ) ?

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