Worksheet: Sign of a Function

In this worksheet, we will practice determining the sign of a constant, linear, or quadratic function from its equation.

Q1:

In which of the following intervals is 𝑓 ( 𝑥 ) = 8 negative?

  • A ( , 8 )
  • B ( 8 , 8 )
  • C ( 8 , )
  • D ( , )
  • E ( 8 , )

Q2:

For which values of 𝑥 is the function 𝑓 ( 𝑥 ) = 8 𝑥 1 3 positive?

  • A 𝑥 1 3 8
  • B 𝑥 < 1 3 8
  • C 𝑥 1 3 8
  • D 𝑥 > 1 3 8
  • E 𝑥 > 1 3 8

Q3:

Determine the sign of the function 𝑓 ( 𝑥 ) = 2 .

  • AThe function is positive when 𝑥 < 0 , negative when 𝑥 > 0 , and equals zero when 𝑥 = 0 .
  • BThe function is positive when 𝑥 > 0 , negative when 𝑥 < 0 , and equals zero when 𝑥 = 0 .
  • CThe function is positive when 𝑥 { 0 } , and equals zero when 𝑥 = 0 .
  • DThe function is positive for all 𝑥 .

Q4:

Determine the sign of the function 𝑓 ( 𝑥 ) = 1 5 𝑥 in .

  • AThe function is positive for all 𝑥 .
  • BThe function is negative for all 𝑥 .
  • CThe function is positive when 𝑥 > 0 , negative when 𝑥 < 0 , and equals zero when 𝑥 = 0 .
  • DThe function is positive when 𝑥 < 0 , negative when 𝑥 > 0 , and equals zero when 𝑥 = 0 .
  • EThe function is positive when 𝑥 { 0 } , and it equals zero when 𝑥 = 0 .

Q5:

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

  • A The function is positive when 𝑥 > 1 , the function is negative when 𝑥 < 1 , and the function equals zero when 𝑥 = 1 .
  • B The function is positive when 𝑥 > 1 , the function is negative when 𝑥 < 1 , and the function equals zero when 𝑥 = 1 .
  • C The function is positive when 𝑥 < 1 , the function is negative when 𝑥 > 1 , and the function equals zero when 𝑥 = 1 .
  • D The function is positive when 𝑥 < 1 , the function is negative when 𝑥 > 1 , and the function equals zero when 𝑥 = 1 .
  • Epositive

Q6:

Determine the sign of the function 𝑓 ( 𝑥 ) = 5 1 7 𝑥 .

  • AThe function is positive when 𝑥 < 3 5 , negative when 𝑥 > 3 5 , and zero when 𝑥 = 3 5 .
  • BThe function is negative when 𝑥 < 3 5 , positive when 𝑥 > 3 5 , and zero when 𝑥 = 3 5 .
  • CThe function is negative when 𝑥 < 5 , positive when 𝑥 > 5 , and zero when 𝑥 = 5 .
  • DThe function is positive when 𝑥 < 3 5 , negative when 𝑥 > 3 5 , and zero when 𝑥 = 3 5 .
  • EThe function is positive when 𝑥 { 5 } , and zero when 𝑥 = 5 .

Q7:

Which of the following statements about the sign of the function 𝑓 ( 𝑥 ) = ( 𝑥 + 3 ) 2 is correct?

  • A 𝑓 ( 𝑥 ) is negative for 𝑥 3 .
  • B 𝑓 ( 𝑥 ) is positive for 𝑥 3 .
  • C 𝑓 ( 𝑥 ) is negative for 𝑥 3 .
  • D 𝑓 ( 𝑥 ) is positive for 𝑥 3 .
  • E 𝑓 ( 𝑥 ) is positive for 𝑥 9 .

Q8:

Determine the sign of the function 𝑓 ( 𝑥 ) = ( 𝑥 8 ) ( 𝑥 7 ) .

  • A The function is positive when 𝑥 { 7 , 8 } , the function is negative when 𝑥 [ 7 , 8 ] , and the function equals zero when 𝑥 { 7 , 8 } .
  • B The function is positive when 𝑥 ( 7 , 8 ) , the function is negative when 𝑥 [ 7 , 8 ] , and the function equals zero when 𝑥 { 7 , 8 } .
  • C The function is positive when 𝑥 [ 7 , 8 ] , the function is negative when 𝑥 { 7 , 8 } , and the function equals zero when 𝑥 { 7 , 8 } .
  • D The function is positive when 𝑥 [ 7 , 8 ] , the function is negative when 𝑥 ( 7 , 8 ) , and the function equals zero when 𝑥 { 7 , 8 } .

Q9:

The function 𝑓 ( 𝑥 ) = ( 𝑥 1 ) ( 𝑥 + 6 ) is positive in which interval?

  • A ( 1 , 6 )
  • B [ 1 , 6 ]
  • C ( 1 , 6 )
  • D ( 6 , 1 )
  • E [ 6 , 1 ]

Q10:

Determine the sign of the function 𝑓 ( 𝑥 ) = 4 2 5 𝑥 .

  • AThe function is positive for all 𝑥 2 5 , and equals zero when 𝑥 = 2 5 .
  • BThe function is negative at 𝑥 2 5 , 2 5 , positive at 𝑥 2 5 , 2 5 , and equals zero when 𝑥 2 5 , 2 5 .
  • CThe function is positive for all 𝑥 { 2 } , and equals zero when 𝑥 = 2 .
  • DThe function is positive at 𝑥 2 5 , 2 5 , negative at 𝑥 2 5 , 2 5 , and equals zero when 𝑥 2 5 , 2 5 .

Q11:

Determine the sign of the function 𝑓 ( 𝑥 ) = 𝑥 + 1 0 𝑥 + 1 6 .

  • A The function is positive when 𝑥 { 8 , 2 } , the function is negative when 𝑥 [ 8 , 2 ] , and the function equals zero when 𝑥 { 8 , 2 } .
  • B The function is positive when 𝑥 ( 8 , 2 ) , the function is negative when 𝑥 [ 8 , 2 ] , and the function equals zero when 𝑥 { 8 , 2 } .
  • C The function is positive when 𝑥 [ 8 , 2 ] , the function is negative when 𝑥 { 8 , 2 } , and the function equals zero when 𝑥 { 8 , 2 } .
  • D The function is positive when 𝑥 [ 8 , 2 ] , the function is negative when 𝑥 ( 8 , 2 ) , and the function equals zero when 𝑥 { 8 , 2 } .

Q12:

Determine the sign of the function 𝑓 ( 𝑥 ) = 𝑥 1 6 𝑥 + 6 4 .

  • AThe function is positive for all 𝑥 .
  • BThe function is positive when 𝑥 { 8 } , and the function equals zero when 𝑥 = 8 .
  • CThe function is positive when 𝑥 { 8 , 8 } , and the function equals zero when 𝑥 { 8 , 8 } .
  • DThe function is positive when 𝑥 { 8 } , and the function equals zero when 𝑥 = 8 .
  • EThe function is positive when 𝑥 { 8 } , and the function equals zero when 𝑥 = 8 .

Q13:

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

  • AThe function is positive for all 𝑥 { 0 } , and the function equals zero when 𝑥 = 0 .
  • BThe function is positive for all 𝑥 .
  • CThe function is negative for all 𝑥 { 0 } , and the function equals zero when 𝑥 = 0 .
  • DThe function is negative for all 𝑥 .

Q14:

Determine the sign of the function 𝑓 ( 𝑥 ) = 7 𝑥 + 1 6 7 𝑥 + 6 4 in .

  • AThe function is positive when 𝑥 8 7 and is zero when 𝑥 = 8 7 .
  • BThe function is negative when 𝑥 8 7 and is zero when 𝑥 = 8 7 .
  • CThe function is negative when 𝑥 8 7 and is zero when 𝑥 = 8 7 .
  • DThe function is positive when 𝑥 8 7 and is zero when 𝑥 = 8 7 .
  • EThe function is positive when 𝑥 7 8 and is zero when 𝑥 = 7 8 .

Q15:

What is the condition on 𝑥 so that 𝑓 ( 𝑥 ) = 3 𝑥 is negative?

  • A 𝑥 𝑔 𝑡 ; 0
  • B 𝑥
  • C 𝑥 { 0 }
  • D 𝑥 < 0

Q16:

Determine where the function 𝑓 ( 𝑥 ) = 𝑥 4 0 0 is positive.

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

Q17:

Determine the interval in which the function 𝑓 ( 𝑥 ) = 1 5 8 𝑥 𝑥 is NOT negative.

  • A [ 5 , 3 ]
  • B [ 3 , 5 ]
  • C [ 3 , 5 ]
  • D [ 5 , 3 ]
  • E

Q18:

What are the values of 𝑥 for which the functions 𝑓 ( 𝑥 ) = 𝑥 5 and 𝑔 ( 𝑥 ) = 𝑥 + 2 𝑥 4 8 are both positive?

  • A 𝑥 < 8
  • B 𝑥 < 6
  • C 𝑥 > 5
  • D 𝑥 > 6
  • E 𝑥 > 8

Q19:

Determine the interval where the sign of each of the two functions 𝑓 ( 𝑥 ) = 2 𝑥 7 𝑥 3 0 and 𝑔 ( 𝑥 ) = 𝑥 3 𝑥 1 0 are negative together on .

  • A , 5 2 ) ( 6 ,
  • B [ 2 , 5 ]
  • C ( 6 , )
  • D ( 2 , 5 )
  • E , 5 2

Q20:

Is there an interval in where the two functions 𝑓 ( 𝑥 ) = 3 𝑥 + 2 6 𝑥 4 0 and 𝑔 ( 𝑥 ) = 9 6 + 4 𝑥 𝑥 are both negative?

  • Ano
  • Byes

Q21:

Find the interval over which the function 𝑓 ( 𝑥 ) = 2 𝑥 is positive.

  • A ( , )
  • B ( , 0 )
  • C ( , ) { 2 }
  • D ( 0 , )

Q22:

Determine the sign of the function 𝑓 [ 1 1 , 1 2 ] , where 𝑓 ( 𝑥 ) = 8 𝑥 .

  • AThe function is negative in the interval [ 1 1 , 8 ) , positive in the interval ( 8 , 1 2 ] , and equals zero at 𝑥 = 8 .
  • BThe function is positive in the interval [ 1 1 , 8 ] , negative in the interval [ 8 , 1 2 ] , and equals zero at 𝑥 = 8 .
  • CThe function is positive in the interval ( , 8 ) , negative in the interval ( 8 , ] , and equals zero at 𝑥 = 8 .
  • DThe function is positive in the interval [ 1 1 , 8 ) , negative in the interval ( 8 , 1 2 ] , and equals zero at 𝑥 = 8 .
  • EThe function is positive in the interval ( , 8 ) , negative in the interval ( 8 , ] , and equals zero at 𝑥 = 8 .

Q23:

Find the sign of the function 𝑓 ( 𝑥 ) = 5 across its domain.

  • A 𝑓 ( 𝑥 ) is positive for 𝑥 { 0 } .
  • B 𝑓 ( 𝑥 ) is negative for 𝑥 .
  • C 𝑓 ( 𝑥 ) is negative for 𝑥 { 0 } .
  • D 𝑓 ( 𝑥 ) is positive for 𝑥 .
  • E 𝑓 ( 𝑥 ) is positive for 𝑥 > 0 .

Q24:

Given a real, nonzero number 𝑎 , what can you say about the sign of the function 𝑓 ( 𝑥 ) = 𝑎 for any real value of 𝑥 ?

  • AIt is always negative.
  • BIt is always positive.
  • CIt is always the same sign as 𝑎 .

Q25:

Determine the sign of the function 𝑓 ( 𝑥 ) = 𝑥 + ( 𝑥 2 ) ( 6 𝑥 + 3 ) + 2 ( 𝑥 + 2 ) + 2 in .

  • AThe function is positive when 𝑥 { 0 } and equals zero when 𝑥 = { 0 } .
  • BThe function is negative when 𝑥 ( 0 , 1 ) , the function equals zero when 𝑥 = { 0 , 1 } , and the function is positive when 𝑥 ( 0 , 1 ) .
  • CThe function is negative when 𝑥 { 0 } and equals zero when 𝑥 = { 0 } .
  • DThe function is positive when 𝑥 ( 0 , 1 ) , the function equals zero when 𝑥 = { 0 , 1 } , and the function is negative when 𝑥 ( 0 , 1 ) .
  • EThe function is positive when 𝑥 { 1 } and equals zero when 𝑥 = { 1 } .

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