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Worksheet: Analyzing Rational Functions

Practice finding the domain and range of a rational function from its graph or from its defining rule. This worksheet includes questions where the numerator and denominator of the rational function have factors in common.

Q1:

Simplify the function , and find its domain.

  • A, domain
  • B, domain
  • C, domain
  • D, domain
  • E, domain

Q2:

Simplify the function , and find its domain.

  • A, domain
  • B, domain
  • C, domain
  • D, domain
  • E, domain

Q3:

Simplify the function , and find its domain.

  • A, domain
  • B, domain
  • C, domain
  • D, domain
  • E, domain

Q4:

Identify the domain of .

  • A
  • B
  • C
  • D
  • E

Q5:

Simplify the function , and determine its domain.

  • A, domain
  • B, domain
  • C, domain
  • D, domain
  • E, domain

Q6:

Determine the domain of the function .

  • A
  • B
  • C
  • D
  • E

Q7:

Find the domain of the function .

  • A
  • B
  • C
  • D

Q8:

Find the domain of the function .

  • A
  • B
  • C
  • D

Q9:

Determine the domain and the range of the function represented in the shown figure.

  • AThe domain is , and the range is .
  • BThe domain is , and the range is .
  • CThe domain is , and the range is .
  • DThe domain is , and the range is .
  • EThe domain is , and the range is .

Q10:

Determine the domain and the range of the function represented in the shown figure.

  • AThe domain is , and the range is .
  • BThe domain is , and the range is .
  • CThe domain is , and the range is .
  • DThe domain is , and the range is .
  • EThe domain is , and the range is .

Q11:

Find the domain and range of the function .

  • AThe domain is and the range is .
  • BThe domain is and the range is .
  • CThe domain is and the range is .
  • DThe domain is and the range is .

Q12:

Determine the domain and the range of the function in .