Lesson Worksheet: Radical Functions Mathematics

In this worksheet, we will practice graphing radical functions and then analyzing the function’s domain, range, intercepts, end behavior, continuity, and decreasing and increasing intervals.

Q1:

Find the domain of the function 𝑓(𝑥)=√7𝑥−7.

  • Aℝ−[1,∞)
  • Bℝ−{1}
  • C[1,∞)
  • D[−1,∞)
  • E(−∞,1]

Q2:

What is the domain of the function √𝑥?

  • Arational numbers
  • Bnonnegative real numbers
  • Cintegers
  • Dall real numbers

Q3:

Find the domain of the function 𝑓(𝑥)=√−55−7𝑥 in ℝ.

  • Aℝ−−557
  • B−∞,−557
  • C−557,∞
  • D−∞,−557

Q4:

Find the domain of the function 𝑓(𝑥)=√𝑥−27.

  • Aℝ
  • B[−27,∞)
  • C[0,∞)
  • Dℝ
  • Eℝ

Q5:

Determine the domain of the function 𝑓(𝑥)=√−8𝑥+16.

  • A[−2,∞)
  • B(−∞,0]
  • Cℝ
  • Dℝ
  • Eℝ

Q6:

What is the domain of the function 𝑓(𝑥)=√1−𝑥?

  • A𝑥<1
  • B𝑥≤2
  • C𝑥≥2
  • D𝑥≤1
  • E𝑥≥1

Q7:

Determine the domain of the function 𝑓(𝑥)=√𝑥+5𝑥−5.

  • A(5,∞)
  • B[−5,∞)
  • C[−5,∞)−{5}
  • D[−5,5)
  • E(−5,∞)−{5}

Q8:

Find the domain of the function 𝑓(𝑥)=6√253𝑥+498𝑥+224.

  • Aℝ−−1411,−1623
  • B−1411,−1623
  • Cℝ−−1411,−1623
  • D−1411,−1623
  • Eℝ−−1411,−1623

Q9:

Determine the domain of the function 𝑓(𝑥)=√5−𝑥√𝑥+2.

  • A[−2,5]
  • B(−2,5]
  • C(−2,5)
  • D(−2,∞)
  • E[5,∞)

Q10:

Determine the domain of the function 𝑓(𝑥)=5𝑥√3𝑥−5 in ℝ.

  • A−∞,53
  • B(5,∞)
  • C53,∞
  • Dℝ−53
  • E53,∞

Q11:

Find the domain of the function 𝑓(𝑥)=3√294+175𝑥−304𝑥.

  • Aℝ−−1419,2116
  • B−1419,2116
  • Cℝ−−1419,2116
  • Dℝ−−1419,2116
  • E−1419,2116

Q12:

Determine the domain of the function 𝑓(𝑥)=√𝑥+7√𝑥−5.

  • A[−7,∞)
  • B(5,∞)
  • C[5,∞)
  • D[−7,∞)−{5}
  • E[−7,5)

Q13:

If 𝑓 and 𝑔 are two real functions where 𝑓(𝑥)=𝑥+𝑥 and 𝑔(𝑥)=√𝑥+5, find the domain of the function 𝑓𝑔.

  • A[−5,∞)−{0,−1}
  • Bℝ−{0,−1}
  • C[−5,∞)
  • D(−5,∞)
  • E(−∞,−5]

Q14:

Find the domain of the function 𝑓(𝑥)=6√9−25𝑥 in ℝ.

  • A−35,35
  • B−35,35
  • Cℝ−−35,35
  • D−∞,−35

Q15:

Determine the domain of the function 𝑓(𝑥)=√𝑥+1𝑥−16.

  • A[−1,∞)−{4}
  • B(−1,∞)
  • C[−1,∞)−{16}
  • D(−1,∞)−{4}
  • E(−∞,−1]−{−4}

Q16:

If 𝑓 and 𝑔 are two real functions where 𝑓(𝑥)=𝑥−4 and 𝑔(𝑥)=√8−𝑥, determine the domain of the function 𝑔𝑓.

  • Aℝ−{2,−2}
  • B(−∞,8]−{2,−2}
  • C[8,∞)
  • D(−∞,8)−{2,−2}
  • E(−∞,8)

Q17:

Find the domain of the function 𝑓(𝑥)=6√−99−8𝑥.

  • Aℝ−−998
  • B−998,∞
  • C−∞,−998
  • D−998,∞
  • E−∞,−998

Q18:

Determine the domain of the function 𝑓(𝑥)=2√86−|𝑥|.

  • Aℝ−[−86,86]
  • B[−86,86]
  • Cℝ−(−86,86)
  • D(−86,86)

Q19:

What is the domain of the function 𝑓(𝑥)=(1−𝑥)?

  • A𝑥≤2
  • B𝑥≤1
  • C𝑥≤0
  • D𝑥>1
  • E𝑥>2

Q20:

Determine the domain of the function 𝑓(𝑥)=√4𝑥+3.

  • A−∞,−34
  • Bℝ−−34
  • Cℝ
  • Dℝ−34
  • E−34,∞

Q21:

Determine the domain of the function 𝑓(𝑥)=√27−|𝑥|.

  • A[−27,27]
  • Bℝ−[−27,27]
  • Cℝ−(−27,27)
  • D(−27,27)

Q22:

What is the domain of the function 𝑓(𝑥)=(1−𝑥)?

  • A𝑥≥2
  • Ball real numbers
  • C𝑥≤1
  • D𝑥≥1
  • E𝑥<1

Q23:

Find the domain of the function 𝑓(𝑥)=√10+11𝑥−35𝑥.

  • A−25,57
  • Bℝ−−25,57
  • Cℝ−−25,57
  • Dℝ−−25,57
  • E−25,57

Q24:

Find the domain of the function 𝑓(𝑥)=√324−𝑥.

  • Aℝ−(−18,18)
  • Bℝ−{−18,18}
  • Cℝ−[−18,18]
  • D(−18,18)
  • E[−18,18]

Q25:

Determine the domain of the function 𝑓(𝑥)=√256𝑥+121.

  • Aℝ−−1116,1116
  • Bℝ
  • C−1116,1116
  • Dℝ−−1116,1116
  • Eℝ−−1116,1116

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