Worksheet: Domain and Range of Square Root Functions

In this worksheet, we will practice analyzing square root functions, graphing them, finding their domains and ranges, and using them to solve real-world problems.

Q1:

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

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

Q2:

What is the domain of the function 𝑥 ?

  • Arational numbers
  • Ball real numbers
  • Cintegers
  • Dnonnegative real numbers

Q3:

Find the domain of the function 𝑓 ( 𝑥 ) = 5 5 7 𝑥 in .

  • A 5 5 7 ,
  • B , 5 5 7
  • C 5 5 7
  • D , 5 5 7

Q4:

Find the domain of the function 𝑓 ( 𝑥 ) = 𝑥 2 7 .

  • A
  • B
  • C
  • D [ 0 , )
  • E [ 2 7 , )

Q5:

Determine the domain of the function 𝑓 ( 𝑥 ) = 8 𝑥 + 1 6 .

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

Q6:

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

  • A 𝑥 1
  • B 𝑥 2
  • C 𝑥 2
  • D 𝑥 1
  • E 𝑥 < 1

Q7:

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

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

Q8:

Find the domain of the function 𝑓 ( 𝑥 ) = 6 2 5 3 𝑥 + 4 9 8 𝑥 + 2 2 4 .

  • A 1 4 1 1 , 1 6 2 3
  • B 1 4 1 1 , 1 6 2 3
  • C 1 4 1 1 , 1 6 2 3
  • D 1 4 1 1 , 1 6 2 3
  • E 1 4 1 1 , 1 6 2 3

Q9:

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

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

Q10:

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

  • A , 5 3
  • B 5 3 ,
  • C ( 5 , )
  • D 5 3 ,
  • E 5 3

Q11:

Find the domain of the function 𝑓 ( 𝑥 ) = 3 2 9 4 + 1 7 5 𝑥 3 0 4 𝑥 .

  • A 1 4 1 9 , 2 1 1 6
  • B 1 4 1 9 , 2 1 1 6
  • C 1 4 1 9 , 2 1 1 6
  • D 1 4 1 9 , 2 1 1 6
  • E 1 4 1 9 , 2 1 1 6

Q12:

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

  • A [ 7 , )
  • B [ 5 , )
  • C [ 7 , 5 )
  • D ( 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 𝑓 𝑔 .

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

Q14:

Find the domain of the function 𝑓 ( 𝑥 ) = 6 9 2 5 𝑥 in .

  • A 3 5 , 3 5
  • B 3 5 , 3 5
  • C , 3 5
  • D 3 5 , 3 5

Q15:

Determine the domain of the function 𝑓 ( 𝑥 ) = 𝑥 + 1 𝑥 1 6 .

  • A ( 1 , ) { 4 }
  • B ( 1 , )
  • C [ 1 , ) { 1 6 }
  • 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 𝑔 𝑓 .

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

Q17:

Find the domain of the function 𝑓 ( 𝑥 ) = 6 9 9 8 𝑥 .

  • A 9 9 8 ,
  • B , 9 9 8
  • C 9 9 8
  • D , 9 9 8
  • E 9 9 8 ,

Q18:

Determine the domain of the function 𝑓 ( 𝑥 ) = 2 8 6 | 𝑥 | .

  • A [ 8 6 , 8 6 ]
  • B [ 8 6 , 8 6 ]
  • C ( 8 6 , 8 6 )
  • D ( 8 6 , 8 6 )

Q19:

Give the domain of the function .

  • A
  • B
  • C
  • D
  • E

Q20:

Given the function 𝑡 ( 𝑠 ) = 1 5 𝑥 1 3 , evaluate 𝑡 ( 9 ) .

Q21:

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

  • A 𝑥 0
  • B 𝑥 2
  • C 𝑥 > 1
  • D 𝑥 1
  • E 𝑥 > 2

Q22:

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

  • A 3 4
  • B 3 4
  • C , 3 4
  • D
  • E 3 4 ,

Q23:

Determine the domain of the function 𝑓 ( 𝑥 ) = 2 7 | 𝑥 | .

  • A [ 2 7 , 2 7 ]
  • B ( 2 7 , 2 7 )
  • C ( 2 7 , 2 7 )
  • D [ 2 7 , 2 7 ]

Q24:

What is the domain of the function 𝑓 ( 𝑥 ) = ( 1 𝑥 ) 2 3 ?

  • A 𝑥 1
  • B 𝑥 1
  • C 𝑥 2
  • Dall real numbers
  • E 𝑥 < 1

Q25:

Find the domain of the function 𝑓 ( 𝑥 ) = 1 0 + 1 1 𝑥 3 5 𝑥 .

  • A 2 5 , 5 7
  • B 2 5 , 5 7
  • C 2 5 , 5 7
  • D 2 5 , 5 7
  • E 2 5 , 5 7

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