Worksheet: Polynomial Functions

In this worksheet, we will practice identifying, writing, and evaluating a one-variable polynomial function and stating its degree and leading coefficient.

Q1:

Find the value of 𝑓(8) given the function 𝑓(𝑥)=37𝑥.

Q2:

Evaluate 𝑓57 given that 𝑓(𝑥)=3𝑥+34.

  • A 2 1 7
  • B 2 2 5 2 8
  • C 3 3 4
  • D 1 1 3 2 8
  • E 1 1 7 2 8

Q3:

Find the value of 𝑓(8) given the function 𝑓(𝑥)=𝑥14.

Q4:

Find the value of 𝑓(14) given the function 𝑓(𝑥)=𝑥28𝑥+7.

Q5:

Find the value of 𝑓2 given the function 𝑓(𝑥)=𝑥+2𝑥.

Q6:

If 𝑓(𝑥)=8𝑥3𝑥+4, find 𝑓(3).

Q7:

Complete the given table of values for the function 𝑦=5𝑥2.

𝑥 2 1 0 1 2
𝑦
  • A 4 0 , 5 , 5 , 5 , 4 0
  • B 1 0 , 3 , 2 , 3 , 3 8
  • C 4 2 , 7 , 2 , 3 , 3 8
  • D 8 , 1 , 2 , 1 , 1 0
  • E 3 8 , 3 , 2 , 5 , 4 0

Q8:

Find 𝑓(3)+𝑓(5) given 𝑓(𝑥)=𝑥.

Q9:

Given the function 𝑡(𝑠)=𝑠4𝑠, evaluate 𝑡(4).

Q10:

Find the value of 𝑓(5) given the function 𝑓(𝑥)=𝑥23𝑥+31.

Q11:

If 𝑓(𝑥)=6𝑥+6𝑥+8, find 𝑓(2).

Q12:

Consider the polynomial function 𝑓(𝑥)=7𝑥+2𝑥+𝑥2𝑥+2.

Evaluate 𝑓(2).

Evaluate 𝑓(2).

Q13:

Consider the polynomial function 𝑓(𝑥)=2𝑥+5𝑥7𝑥+10. Evaluate 𝑓𝑥+1.

  • A 2 𝑥 + 9 𝑥 + 2 𝑥 + 1 0
  • B 2 𝑥 + 1 1 𝑥 + 2 3 𝑥 + 2 4
  • C 2 𝑥 + 5 𝑥 + 7 𝑥 + 2 4
  • D 2 𝑥 + 1 1 𝑥 + 9 𝑥 + 1 0
  • E 2 𝑥 + 5 𝑥 7 𝑥 + 1 0

Q14:

Consider the function 𝑓(𝑥)=𝑥3𝑥4. Find 𝑓(𝑥+3).

  • A 𝑓 ( 𝑥 + 3 ) = 𝑥 3 𝑥
  • B 𝑓 ( 𝑥 + 3 ) = 𝑥 3 𝑥 1
  • C 𝑓 ( 𝑥 + 3 ) = 𝑥 + 3 𝑥 + 1
  • D 𝑓 ( 𝑥 + 3 ) = 𝑥 + 3 𝑥 4

Q15:

A polynomial function that has three different roots .

  • Apasses both the vertical and the horizontal line tests
  • Bwill have no more than two relative maximums
  • Cwill have no more than two relative minimums
  • Dcan be inverted only if the domain is restricted

Q16:

The given graph is of a polynomial 𝑓.

What is the degree of 𝑓?

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