Worksheet: Graphs of Polynomial Functions

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)=(𝑥2)?

  • A
  • B
  • C
  • D
  • E

Q2:

Which of the following is the graph of 𝑓(𝑥)=(𝑥2)(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)=(𝑥3)(𝑥+1)(𝑥+4)?

  • A
  • B
  • C
  • D
  • E

Q5:

Which of the following is the graph of 𝑓(𝑥)=(𝑥1)(𝑥+1)?

  • A
  • B
  • C
  • D
  • E

Q6:

Which of the following is the graph of 𝑓(𝑥)=(𝑥+3)(𝑥1)(𝑥+2)(𝑥2)?

  • A
  • B
  • C
  • D
  • E

Q7:

Which of the following is the graph of 𝑓(𝑥)=(𝑥+1)(𝑥2)(𝑥1)?

  • A
  • B
  • C
  • D
  • E

Q8:

Which of the following is the graph of 𝑓(𝑥)=(𝑥+3)(𝑥1)(𝑥+2)(𝑥2)?

  • 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)(𝑥5)(𝑥7)(𝑥9)
  • B2(𝑥+1)(𝑥5)(𝑥7)(𝑥9)
  • C5(𝑥+3)(𝑥1)(𝑥2)(𝑥7)
  • D5(𝑥+3)(𝑥1)(𝑥2)(𝑥+7)
  • E(𝑥+3)(𝑥1)(𝑥2)(𝑥7)

Q10:

Which of the following is the graph of 𝑓(𝑥)=(𝑥+3)(𝑥1)(𝑥4)?

  • A
  • B
  • C
  • D
  • E

Q11:

Which of the following is the graph of 𝑓(𝑥)=(𝑥3)(𝑥+1)(𝑥+4)?

  • A
  • B
  • C
  • D
  • E

Q12:

Which of the following is the graph of 𝑓(𝑥)=(𝑥3)(𝑥+1)(𝑥+2)(𝑥2)?

  • A
  • B
  • C
  • D
  • E

Q13:

Which of the following is the graph of 𝑓(𝑥)=(𝑥+2)(𝑥2)?

  • A
  • B
  • C
  • D
  • E

Q14:

Which of the following is the graph of 𝑓(𝑥)=(𝑥+2)(𝑥2)?

  • A
  • B
  • C
  • D
  • E

Q15:

Which of the following is the graph of 𝑓(𝑥)=(𝑥2)(𝑥+2)?

  • A
  • B
  • C
  • D
  • E

Q16:

Solve 𝑥4𝑥+4=0 by factoring, and hence determine which of the following figures would be a sketch of 𝑦=𝑥4𝑥+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)(𝑥2), 𝑔(𝑥)=25(𝑥4), and their product 𝑃(𝑥)=25(𝑥+1)(𝑥2)(𝑥4) are represented. What is the function if (b) is the graph 𝑦=(𝑥)𝑃(𝑥)?

  • A(𝑥)=𝑥1
  • B(𝑥)=𝑥1
  • C(𝑥)=1𝑥
  • D(𝑥)=𝑥1
  • E(𝑥)=1𝑥

Q19:

Which of the following is the graph of 𝑓(𝑥)=(𝑥3)(𝑥+1)(𝑥+2)(𝑥2)?

  • A
  • B
  • C
  • D
  • E

Q20:

Which of the following is the graph of 𝑓(𝑥)=(𝑥1)(𝑥+1)(𝑥2)?

  • 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+𝑥6=0 by factoring, and hence determine which of the following figures would be a sketch of 𝑦=𝑥+𝑥6.

  • 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=(𝑥1)(𝑥+3)(𝑥3)
  • C𝑦=(𝑥+1)(𝑥+3)(𝑥3)
  • D𝑦=(𝑥+1)(𝑥+3)(𝑥3)
  • E𝑦=(𝑥1)(𝑥+3)(𝑥3)

Q25:

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

  • A𝑦=(𝑥2)(𝑥+5)
  • B𝑦=(𝑥+2)(𝑥5)
  • C𝑦=(𝑥+2)(𝑥+5)
  • D𝑦=(𝑥2)(𝑥+5)
  • E𝑦=(𝑥+2)(𝑥5)

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