Lesson Worksheet: Domain of Rational Functions Mathematics

In this worksheet, we will practice identifying the domain of a rational function and the common domain of two or more rational functions.


Identify the domain of 𝑛(𝑥)=9𝑥+83𝑥+2.

  • A23
  • B23
  • C32
  • D32
  • E89,23


For which values of 𝑥 is the function 𝑛(𝑥)=𝑥25𝑥12𝑥+32 not defined?

  • A{4,8}
  • B{8,4}
  • C{5,5}
  • D{4,8}
  • E{5,5}


What is the domain of the function 𝑦=𝑥1𝑥+1?

  • A{1}
  • B, the positive real numbers
  • C
  • D{1}
  • E{1,1}


Find the domain of the function 𝑓(𝑥)=𝑥16𝑥𝑥4𝑥.

  • A{0,4}
  • B{0,4}
  • C{4,8}
  • D
  • E[0,4]


Find the domain of the real function 𝑓(𝑥)=𝑥+48𝑥343.

  • A{7}
  • B{48}
  • C{7}
  • D{48}


Find the common domain between the functions 𝑛(𝑥)=9𝑥+9, 𝑛(𝑥)=8𝑥+3, and 𝑛(𝑥)=7𝑥𝑥4𝑥.

  • A{9,3,2}
  • B{9,3,2,0,2}
  • C{9,3,0,2}
  • D{9,3,2,2}
  • E{2,0,2,3,9}


Find 𝑘, given the domain of the function 𝑛(𝑥)=7𝑥+𝑘 is {4}.


If the domain of the function 𝑓(𝑥)=5𝑥8𝑥+𝑘 is {4}, determine the value of 𝑘.

  • A𝑘=16
  • B𝑘=4
  • C𝑘=16
  • D𝑘=4


Given that the domain of the function 𝑛(𝑥)=36𝑥+20𝑥+𝑎 is {2,0}, evaluate 𝑛(3).


If the common domain of the two functions 𝑛(𝑥)=𝑥𝑥+64 and 𝑛(𝑥)=5𝑥+11𝑥𝑏 is {7,4}, find the value of 𝑏.

This lesson includes 36 additional questions and 385 additional question variations for subscribers.

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