Lesson Worksheet: Domain and Range of a Rational Function Mathematics • 10th Grade

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In this worksheet, we will practice finding the domain and range of a rational function either from its graph or its defining rule.

Q1:

Find the value of 𝑐 given 𝑛(𝑥)=1425𝑥+60𝑥+36 where 𝑛(𝑐) is undefined.

  • A56
  • B−65
  • C−56
  • D14
  • E65

Q2:

Determine the domain and the range of the function 𝑓(𝑥)=1𝑥−2.

  • AThe domain is ℝ−{2}, and the range is ℝ−{0}.
  • BThe domain is {0}, and the range is ℝ.
  • CThe domain is ℝ, and the range is ℝ.
  • DThe domain is ℝ, and the range is {2}.

Q3:

Simplify the function 𝑓(𝑥)=𝑥+7𝑥−8𝑥𝑥−65𝑥+64, and find its domain.

  • A𝑓(𝑥)=𝑥(𝑥+1)(𝑥−8), domain =ℝ−{1,−1,−8,8}
  • B𝑓(𝑥)=𝑥(𝑥+7𝑥−8)(𝑥−1)(𝑥−64), domain =ℝ−{1,−1,−8,8}
  • C𝑓(𝑥)=𝑥(𝑥−1)(𝑥+8), domain =ℝ−{1,−8}
  • D𝑓(𝑥)=𝑥(𝑥+1)(𝑥−8), domain =ℝ−{−1,8}
  • E𝑓(𝑥)=𝑥(𝑥−1)(𝑥+8), domain =ℝ−{1,−1,−8,8}

Q4:

Find the domain of the function 𝑓(𝑥)=𝑥+4(𝑥−8).

  • Aℝ−{−4,8}
  • Bℝ−{8}
  • Cℝ−{−8,8}
  • Dℝ−{−4}

Q5:

The domain of an algebraic fractional function is the set of all real numbers except the .

  • Azeros of the function
  • Bzeros of the denominator of the function

Q6:

Determine the domain and the range of the function 𝑓(𝑥)=𝑥−16𝑥+4.

  • AThe domain is {−4} and the range is ℝ.
  • BThe domain is ℝ−{−4} and the range is ℝ−{−8}.
  • CThe domain is ℝ and the range is {−4}.
  • DThe domain is ℝ−{−8} and the range is ℝ−{−4}.
  • EThe domain is {−8,−4} and the range is ℝ.

Q7:

Define a function on real numbers by 𝑓(𝑥)=2𝑥+34𝑥+5.

What is the domain of this function?

  • Aall real numbers except 54
  • Ball real numbers except 32
  • Call real numbers except −54
  • Dall real numbers except −32
  • Eall real numbers

Find the one value that 𝑓(𝑥) cannot take.

  • A12
  • B−54
  • C54
  • D−32
  • E−12

What is the range of this function?

  • Aall real numbers except −32
  • Ball real numbers
  • Call real numbers except −54
  • Dall real numbers except 12
  • Eall real numbers except −12

Q8:

Determine the domain and the range of the function 𝑓(𝑥)=1|𝑥−2|.

  • AThe domain is ]0,∞[ and the range is ℝ−{2}.
  • BThe domain is {2} and the range is ℝ.
  • CThe domain is ℝ and the range is {2}.
  • DThe domain is ℝ−{2} and the range is ]0,∞[.

Q9:

Identify the domain of 𝑛(𝑥)=9𝑥+83𝑥+2.

  • Aℝ−−23
  • Bℝ−23
  • Cℝ−−32
  • Dℝ−32
  • Eℝ−−89,−23

Q10:

The function 𝑓(𝑥)=𝑥−2𝑥−1 has an additive inverse if the domain is .

  • Aℝ−{−1}
  • Bℝ−{1,2}
  • Cℝ−{−2}
  • Dℝ−{1}
  • Eℝ−{2}

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