Worksheet: Radical Functions

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)=7𝑥7.

  • A[1,)
  • B{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)=557𝑥 in .

  • A557
  • B,557
  • C557,
  • D,557

Q4:

Find the domain of the function 𝑓(𝑥)=𝑥27.

  • A
  • B[27,)
  • C[0,)
  • D
  • E

Q5:

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

  • A[2,)
  • B(,0]
  • C
  • D
  • E

Q6:

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

  • A𝑥<1
  • B𝑥2
  • C𝑥2
  • D𝑥1
  • E𝑥1

Q7:

Determine the domain of the function 𝑓(𝑥)=𝑥+5𝑥5.

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

Q8:

Find the domain of the function 𝑓(𝑥)=6253𝑥+498𝑥+224.

  • A1411,1623
  • B1411,1623
  • C1411,1623
  • D1411,1623
  • E1411,1623

Q9:

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

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

Q10:

Determine the domain of the function 𝑓(𝑥)=5𝑥3𝑥5 in .

  • A,53
  • B(5,)
  • C53,
  • D53
  • E53,

Q11:

Find the domain of the function 𝑓(𝑥)=3294+175𝑥304𝑥.

  • A1419,2116
  • B1419,2116
  • C1419,2116
  • D1419,2116
  • E1419,2116

Q12:

Determine the domain of the function 𝑓(𝑥)=𝑥+7𝑥5.

  • 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}
  • B{0,1}
  • C[5,)
  • D(5,)
  • E(,5]

Q14:

Find the domain of the function 𝑓(𝑥)=6925𝑥 in .

  • A35,35
  • B35,35
  • C35,35
  • D,35

Q15:

Determine the domain of the function 𝑓(𝑥)=𝑥+1𝑥16.

  • 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)=𝑥4 and 𝑔(𝑥)=8𝑥, determine the domain of the function 𝑔𝑓.

  • A{2,2}
  • B(,8]{2,2}
  • C[8,)
  • D(,8){2,2}
  • E(,8)

Q17:

Find the domain of the function 𝑓(𝑥)=6998𝑥.

  • A998
  • B998,
  • C,998
  • D998,
  • E,998

Q18:

Determine the domain of the function 𝑓(𝑥)=286|𝑥|.

  • A[86,86]
  • B[86,86]
  • C(86,86)
  • D(86,86)

Q19:

Give the domain of the function 𝑓(𝑥)=𝑥+2𝑥.

  • A(,2](0,)
  • B(2,)
  • C(,0]
  • D(0,)
  • E(,2]

Q20:

Given the function 𝑡(𝑠)=15𝑥1, evaluate 𝑡(9).

Q21:

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

  • A𝑥2
  • B𝑥1
  • C𝑥0
  • D𝑥>1
  • E𝑥>2

Q22:

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

  • A,34
  • B34
  • C
  • D34
  • E34,

Q23:

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

  • A[27,27]
  • B[27,27]
  • C(27,27)
  • D(27,27)

Q24:

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

  • A𝑥2
  • Ball real numbers
  • C𝑥1
  • D𝑥1
  • E𝑥<1

Q25:

Find the domain of the function 𝑓(𝑥)=10+11𝑥35𝑥.

  • A25,57
  • B25,57
  • C25,57
  • D25,57
  • E25,57

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