Lesson Worksheet: Radical Functions Mathematics • 10th Grade

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(π‘₯)=√7π‘₯βˆ’7.

  • Aβ„βˆ’[1,∞)
  • Bβ„βˆ’{1}
  • C[1,∞)
  • D[βˆ’1,∞)
  • E(βˆ’βˆž,1]

Q2:

What is the domain of the function √π‘₯?

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

Q3:

Find the domain of the function 𝑓(π‘₯)=βˆšβˆ’55βˆ’7π‘₯ in ℝ.

  • Aβ„βˆ’ο¬βˆ’557
  • Bο€Όβˆ’βˆž,βˆ’557
  • Cο”βˆ’557,∞
  • Dο€Όβˆ’βˆž,βˆ’557

Q4:

Find the domain of the function 𝑓(π‘₯)=√π‘₯βˆ’27.

  • Aℝ
  • B[βˆ’27,∞)
  • C[0,∞)
  • Dβ„οŠ±
  • Eβ„οŠ°

Q5:

Determine the domain of the function 𝑓(π‘₯)=βˆšβˆ’8π‘₯+16.

  • A[βˆ’2,∞)
  • B(βˆ’βˆž,0]
  • Cβ„οŠ±
  • Dβ„οŠ°
  • Eℝ

Q6:

What is the domain of the function 𝑓(π‘₯)=√1βˆ’π‘₯?

  • Aπ‘₯<1
  • Bπ‘₯≀2
  • Cπ‘₯β‰₯2
  • Dπ‘₯≀1
  • Eπ‘₯β‰₯1

Q7:

Determine the domain of the function 𝑓(π‘₯)=√π‘₯+5π‘₯βˆ’5.

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

Q8:

Find the domain of the function 𝑓(π‘₯)=6√253π‘₯+498π‘₯+224.

  • Aβ„βˆ’ο€Όβˆ’1411,βˆ’1623
  • Bο€Όβˆ’1411,βˆ’1623
  • Cβ„βˆ’ο”βˆ’1411,βˆ’1623
  • Dο”βˆ’1411,βˆ’1623
  • Eβ„βˆ’ο¬βˆ’1411,βˆ’1623

Q9:

Determine the domain of the function 𝑓(π‘₯)=√5βˆ’π‘₯√π‘₯+2.

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

Q10:

Determine the domain of the function 𝑓(π‘₯)=5π‘₯√3π‘₯βˆ’5 in ℝ.

  • Aο€Όβˆ’βˆž,53
  • B(5,∞)
  • Cο€Ό53,∞
  • Dβ„βˆ’ο¬53
  • E53,∞

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