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(𝑥)=1425𝑥+60𝑥+36 where 𝑛(𝑐) is undefined.

  • A56
  • B65
  • C56
  • D14
  • E65

Q2:

Determine the domain and the range of the function 𝑓(𝑥)=1𝑥2.

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

Q3:

Simplify the function 𝑓(𝑥)=𝑥+7𝑥8𝑥𝑥65𝑥+64, and find its domain.

  • A𝑓(𝑥)=𝑥(𝑥+1)(𝑥8), domain ={1,1,8,8}
  • B𝑓(𝑥)=𝑥(𝑥+7𝑥8)(𝑥1)(𝑥64), domain ={1,1,8,8}
  • C𝑓(𝑥)=𝑥(𝑥1)(𝑥+8), domain ={1,8}
  • D𝑓(𝑥)=𝑥(𝑥+1)(𝑥8), domain ={1,8}
  • E𝑓(𝑥)=𝑥(𝑥1)(𝑥+8), domain ={1,1,8,8}

Q4:

Find the domain of the function 𝑓(𝑥)=𝑥+4(𝑥8).

  • A{4,8}
  • B{8}
  • C{8,8}
  • D{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)=𝑥16𝑥+4.

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

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
  • B54
  • C54
  • D32
  • E12

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|𝑥2|.

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

Q9:

Identify the domain of 𝑛(𝑥)=9𝑥+83𝑥+2.

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

Q10:

The function 𝑓(𝑥)=𝑥2𝑥1 has an additive inverse if the domain is .

  • A{1}
  • B{1,2}
  • C{2}
  • D{1}
  • E{2}

Practice Means Progress

Download the Nagwa Practice app to access 64 additional questions for this lesson!

scan me!

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