Worksheet: Graphs of Polynomial Functions

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

Q1:

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

  • A
  • B
  • C
  • D
  • E

Q2:

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

  • A
  • B
  • C
  • D
  • E

Q3:

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

  • A
  • B
  • C
  • D
  • E

Q4:

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

  • A
  • B
  • C
  • D
  • E

Q5:

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

  • A
  • B
  • C
  • D
  • E

Q6:

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

  • A
  • B
  • C
  • D
  • E

Q7:

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

  • A
  • B
  • C
  • D
  • E

Q8:

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

  • A
  • B
  • C
  • D
  • E

Q9:

The given graph represents a polynomial function.

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

  • A7(𝑥+1)(𝑥−5)(𝑥−7)(𝑥−9)
  • B−2(𝑥+1)(𝑥−5)(𝑥−7)(𝑥−9)
  • C−5(𝑥+3)(𝑥−1)(𝑥−2)(𝑥−7)
  • D−5(𝑥+3)(𝑥−1)(𝑥−2)(𝑥+7)
  • E(𝑥+3)(𝑥−1)(𝑥−2)(𝑥−7)

Q10:

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

  • A
  • B
  • C
  • D
  • E

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+2)(𝑥−2)?

  • A
  • B
  • C
  • D
  • E

Q13:

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

  • A
  • B
  • C
  • D
  • E

Q14:

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

  • A
  • B
  • C
  • D
  • E

Q15:

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

  • A
  • B
  • C
  • D
  • E

Q16:

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

  • A
  • B
  • C
  • D
  • E

Q17:

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

  • A
  • B
  • C
  • D
  • E

Q18:

In (a), the graphs of 𝑓(𝑥)=(𝑥+1)(𝑥−2), 𝑔(𝑥)=−25(𝑥−4), and their product 𝑃(𝑥)=−25(𝑥+1)(𝑥−2)(𝑥−4) are represented. What is the function ℎ if (b) is the graph 𝑦=ℎ(𝑥)𝑃(𝑥)?

  • Aℎ(𝑥)=𝑥−1
  • Bℎ(𝑥)=𝑥−1
  • Cℎ(𝑥)=1−𝑥
  • Dℎ(𝑥)=−𝑥−1
  • Eℎ(𝑥)=1−𝑥

Q19:

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

  • A
  • B
  • C
  • D
  • E

Q20:

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

  • A
  • B
  • C
  • D
  • E

Q21:

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

  • A
  • B
  • C
  • D
  • E

Q22:

Solve 𝑥+𝑥−6=0 by factoring, and hence determine which of the following figures would be a sketch of 𝑦=𝑥+𝑥−6.

  • A
  • B
  • C
  • D
  • E

Q23:

The figure shows the graph of 𝑓(𝑥)=𝑥+2𝑥+3𝑥+4𝑥+5𝑥+𝑥+1.

Determine the quadratic function 𝑔 whose graph is asymptotic to the above.

  • A𝑔(𝑥)=𝑥+𝑥+1
  • B𝑔(𝑥)=𝑥+3𝑥+7
  • C𝑔(𝑥)=𝑥+3𝑥+5
  • D𝑔(𝑥)=𝑥+𝑥+3
  • E𝑔(𝑥)=𝑥+3𝑥+1

Q24:

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

  • A𝑦=−𝑥(𝑥+1)(𝑥+3)
  • B𝑦=−(𝑥−1)(𝑥+3)(𝑥−3)
  • C𝑦=−(𝑥+1)(𝑥+3)(𝑥−3)
  • D𝑦=(𝑥+1)(𝑥+3)(𝑥−3)
  • E𝑦=(𝑥−1)(𝑥+3)(𝑥−3)

Q25:

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

  • A𝑦=−(𝑥−2)(𝑥+5)
  • B𝑦=(𝑥+2)(𝑥−5)
  • C𝑦=−(𝑥+2)(𝑥+5)
  • D𝑦=(𝑥−2)(𝑥+5)
  • E𝑦=−(𝑥+2)(𝑥−5)

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