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

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(π‘₯)=1425π‘₯+60π‘₯+36 where 𝑛(𝑐) is undefined.

  • A56
  • Bβˆ’65
  • Cβˆ’56
  • D14
  • E65

Q2:

Determine the domain and the range of the function 𝑓(π‘₯)=1π‘₯βˆ’2.

  • AThe domain is β„βˆ’{2}, and the range is β„βˆ’{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(π‘₯)=π‘₯+7π‘₯βˆ’8π‘₯π‘₯βˆ’65π‘₯+64οŠͺ, and find its domain.

  • A𝑓(π‘₯)=π‘₯(π‘₯+1)(π‘₯βˆ’8), domain =β„βˆ’{1,βˆ’1,βˆ’8,8}
  • B𝑓(π‘₯)=π‘₯(π‘₯+7π‘₯βˆ’8)(π‘₯βˆ’1)(π‘₯βˆ’64), domain =β„βˆ’{1,βˆ’1,βˆ’8,8}
  • C𝑓(π‘₯)=π‘₯(π‘₯βˆ’1)(π‘₯+8), domain =β„βˆ’{1,βˆ’8}
  • D𝑓(π‘₯)=π‘₯(π‘₯+1)(π‘₯βˆ’8), domain =β„βˆ’{βˆ’1,8}
  • E𝑓(π‘₯)=π‘₯(π‘₯βˆ’1)(π‘₯+8), domain =β„βˆ’{1,βˆ’1,βˆ’8,8}

Q4:

Find the domain of the function 𝑓(π‘₯)=π‘₯+4(π‘₯βˆ’8).

  • Aβ„βˆ’{βˆ’4,8}
  • Bβ„βˆ’{8}
  • Cβ„βˆ’{βˆ’8,8}
  • Dβ„βˆ’{βˆ’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(π‘₯)=π‘₯βˆ’16π‘₯+4.

  • AThe domain is {βˆ’4} and the range is ℝ.
  • BThe domain is β„βˆ’{βˆ’4} and the range is β„βˆ’{βˆ’8}.
  • CThe domain is ℝ and the range is {βˆ’4}.
  • DThe domain is β„βˆ’{βˆ’8} and the range is β„βˆ’{βˆ’4}.
  • EThe domain is {βˆ’8,βˆ’4} and the range is ℝ.

Q7:

Define a function on real numbers by 𝑓(π‘₯)=2π‘₯+34π‘₯+5.

What is the domain of this function?

  • Aall real numbers except 54
  • Ball real numbers except 32
  • Call real numbers except βˆ’54
  • Dall real numbers except βˆ’32
  • Eall real numbers

Find the one value that 𝑓(π‘₯) cannot take.

  • A12
  • Bβˆ’54
  • C54
  • Dβˆ’32
  • Eβˆ’12

What is the range of this function?

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

Q8:

Determine the domain and the range of the function 𝑓(π‘₯)=1|π‘₯βˆ’2|.

  • AThe domain is ]0,∞[ and the range is β„βˆ’{2}.
  • BThe domain is {2} and the range is ℝ.
  • CThe domain is ℝ and the range is {2}.
  • DThe domain is β„βˆ’{2} and the range is ]0,∞[.

Q9:

Identify the domain of 𝑛(π‘₯)=9π‘₯+83π‘₯+2.

  • Aβ„βˆ’ο¬βˆ’23
  • Bβ„βˆ’ο¬23
  • Cβ„βˆ’ο¬βˆ’32
  • Dβ„βˆ’ο¬32
  • Eβ„βˆ’ο¬βˆ’89,βˆ’23

Q10:

The function 𝑓(π‘₯)=π‘₯βˆ’2π‘₯βˆ’1 has an additive inverse if the domain is .

  • Aβ„βˆ’{βˆ’1}
  • Bβ„βˆ’{1,2}
  • Cβ„βˆ’{βˆ’2}
  • Dβ„βˆ’{1}
  • Eβ„βˆ’{2}

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