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Worksheet: Sign of a Function

Q1:

For which values of π‘₯ is the function 𝑓 ( π‘₯ ) = 8 π‘₯ βˆ’ 1 3 positive?

  • A π‘₯ β‰₯ 1 3 8
  • B π‘₯ < 1 3 8
  • C π‘₯ ≀ 1 3 8
  • D π‘₯ > 1 3 8
  • E π‘₯ > βˆ’ 1 3 8

Q2:

For which values of π‘₯ is the function 𝑓 ( π‘₯ ) = βˆ’ 5 π‘₯ + 2 negative?

  • A π‘₯ β‰₯ 2 5
  • B π‘₯ < 2 5
  • C π‘₯ ≀ 2 5
  • D π‘₯ > 2 5
  • E π‘₯ > βˆ’ 2 5

Q3:

Determine the sign of the function 𝑓 ( π‘₯ ) = βˆ’ 1 5 π‘₯ in ℝ .

  • AThe function is positive for all π‘₯ ∈ ℝ .
  • BThe function is negative for all π‘₯ ∈ ℝ .
  • CThe function is positive when π‘₯ > 0 , negative when π‘₯ < 0 , and equals zero when π‘₯ = 0 .
  • DThe function is positive when π‘₯ < 0 , negative when π‘₯ > 0 , and equals zero when π‘₯ = 0 .
  • EThe function is positive when π‘₯ ∈ ℝ βˆ’ { 0 } , and it equals zero when π‘₯ = 0 .

Q4:

Determine the sign of the function 𝑓 ( π‘₯ ) = 7 π‘₯ + 1 6 √ 7 π‘₯ + 6 4 2 in ℝ .

  • AThe function is positive when π‘₯ ∈ ℝ βˆ’  8 √ 7  and is zero when π‘₯ = 8 √ 7 .
  • BThe function is negative when π‘₯ ∈ ℝ βˆ’  βˆ’ 8 √ 7  and is zero when π‘₯ = βˆ’ 8 √ 7 .
  • CThe function is negative when π‘₯ ∈ ℝ βˆ’  8 √ 7  and is zero when π‘₯ = 8 √ 7 .
  • DThe function is positive when π‘₯ ∈ ℝ βˆ’  βˆ’ 8 √ 7  and is zero when π‘₯ = βˆ’ 8 √ 7 .
  • EThe function is positive when π‘₯ ∈ ℝ βˆ’  √ 7 8  and is zero when π‘₯ = √ 7 8 .

Q5:

Determine the sign of the function 𝑓 ( π‘₯ ) = 3 π‘₯ βˆ’ 2 √ 3 π‘₯ + 1 2 in ℝ .

  • AThe function is positive when π‘₯ ∈ ℝ βˆ’  βˆ’ 1 √ 3  and is zero when π‘₯ = βˆ’ 1 √ 3 .
  • BThe function is negative when π‘₯ ∈ ℝ βˆ’  1 √ 3  and is zero when π‘₯ = 1 √ 3 .
  • CThe function is negative when π‘₯ ∈ ℝ βˆ’  βˆ’ 1 √ 3  and is zero when π‘₯ = βˆ’ 1 √ 3 .
  • DThe function is positive when π‘₯ ∈ ℝ βˆ’  1 √ 3  and is zero when π‘₯ = 1 √ 3 .
  • EThe function is positive when π‘₯ ∈ ℝ βˆ’  βˆ’ √ 3  and is zero when π‘₯ = βˆ’ √ 3 .

Q6:

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

  • A The function is positive when π‘₯ > βˆ’ 1 , the function is negative when π‘₯ < βˆ’ 1 , and the function equals zero when π‘₯ = βˆ’ 1 .
  • B The function is positive when π‘₯ > 1 , the function is negative when π‘₯ < 1 , and the function equals zero when π‘₯ = 1 .
  • C The function is positive when π‘₯ < βˆ’ 1 , the function is negative when π‘₯ > βˆ’ 1 , and the function equals zero when π‘₯ = βˆ’ 1 .
  • D The function is positive when π‘₯ < 1 , the function is negative when π‘₯ > 1 , and the function equals zero when π‘₯ = 1 .
  • Epositive

Q7:

Determine the sign of the function 𝑓 ( π‘₯ ) = 2 .

  • AThe function is positive when π‘₯ < 0 , negative when π‘₯ > 0 , and equals zero when π‘₯ = 0 .
  • BThe function is positive when π‘₯ > 0 , negative when π‘₯ < 0 , and equals zero when π‘₯ = 0 .
  • CThe function is positive when π‘₯ ∈ ℝ βˆ’ { 0 } , and equals zero when π‘₯ = 0 .
  • DThe function is positive for all π‘₯ ∈ ℝ .

Q8:

Determine the sign of the function 𝑓 ( π‘₯ ) = βˆ’ 4 .

  • AThe function is positive when π‘₯ < 0 , negative when π‘₯ > 0 , and equals zero when π‘₯ = 0 .
  • BThe function is positive when π‘₯ > 0 , negative when π‘₯ < 0 , and equals zero when π‘₯ = 0 .
  • CThe function is positive when π‘₯ ∈ ℝ βˆ’ { 0 } , and equals zero when π‘₯ = 0 .
  • DThe function is negative for all π‘₯ ∈ ℝ .

Q9:

In which of the following intervals is negative?

  • A
  • B
  • C
  • D
  • E

Q10:

In which of the following intervals is positive?

  • A
  • B
  • C
  • D
  • E

Q11:

Which of the following statements about the sign of the function 𝑓 ( π‘₯ ) = ( π‘₯ + 3 ) 2 is correct?

  • A 𝑓 ( π‘₯ ) is negative for π‘₯ ∈ 3 .
  • B 𝑓 ( π‘₯ ) is positive for π‘₯ ∈ 3 .
  • C 𝑓 ( π‘₯ ) is negative for π‘₯ ∈ βˆ’ 3 .
  • D 𝑓 ( π‘₯ ) is positive for π‘₯ ∈ βˆ’ 3 .
  • E 𝑓 ( π‘₯ ) is positive for π‘₯ ∈ 9 .

Q12:

What is the condition on π‘₯ so that 𝑓 ( π‘₯ ) = 3 π‘₯ is negative?

  • A π‘₯ 𝑔 𝑑 ; 0
  • B π‘₯ ∈ ℝ
  • C π‘₯ ∈ ℝ βˆ’ { 0 }
  • D π‘₯ < 0

Q13:

What is the condition on π‘₯ so that 𝑓 ( π‘₯ ) = 1 1 π‘₯ is positive?

  • A π‘₯ < 0
  • B π‘₯ ∈ ℝ
  • C π‘₯ ∈ ℝ βˆ’ { 0 }
  • D π‘₯ 𝑔 𝑑 ; 0

Q14:

Determine where the function is positive.

  • A
  • B
  • C
  • D
  • E

Q15:

Determine the sign of the function .

  • A The function is positive when , the function is negative when , and the function equals zero when .
  • B The function is positive when , the function is negative when , and the function equals zero when .
  • C The function is positive when , the function is negative when , and the function equals zero when .
  • D The function is positive when , the function is negative when , and the function equals zero when .

Q16:

Determine the sign of the function .

  • A The function is positive when , the function is negative when , and the function equals zero when .
  • B The function is positive when , the function is negative when , and the function equals zero when .
  • C The function is positive when , the function is negative when , and the function equals zero when .
  • D The function is positive when , the function is negative when , and the function equals zero when .

Q17:

Determine the sign of the function 𝑓 ( π‘₯ ) = 5 βˆ’ 1 7 π‘₯ .

  • AThe function is positive when π‘₯ < βˆ’ 3 5 , negative when π‘₯ > βˆ’ 3 5 , and zero when π‘₯ = βˆ’ 3 5 .
  • BThe function is negative when π‘₯ < 3 5 , positive when π‘₯ > 3 5 , and zero when π‘₯ = 3 5 .
  • CThe function is negative when π‘₯ < βˆ’ 5 , positive when π‘₯ > βˆ’ 5 , and zero when π‘₯ = βˆ’ 5 .
  • DThe function is positive when π‘₯ < 3 5 , negative when π‘₯ > 3 5 , and zero when π‘₯ = 3 5 .
  • EThe function is positive when π‘₯ ∈ ℝ βˆ’ { 5 } , and zero when π‘₯ = 5 .

Q18:

What are the values of π‘₯ for which the functions 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 5 and 𝑔 ( π‘₯ ) = π‘₯ + 2 π‘₯ βˆ’ 4 8 2 are both positive?

  • A π‘₯ < βˆ’ 8
  • B π‘₯ < 6
  • C π‘₯ > 5
  • D π‘₯ > 6
  • E π‘₯ > βˆ’ 8

Q19:

The function 𝑓 ( π‘₯ ) = βˆ’ ( π‘₯ βˆ’ 1 ) ( π‘₯ + 6 ) is positive in which interval?

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

Q20:

Determine the interval where the sign of each of the two functions and are negative together on .

  • A
  • B
  • C
  • D
  • E

Q21:

Determine the sign of the function .

  • AThe function is positive for all , and equals zero when .
  • BThe function is negative at , positive at , and equals zero when .
  • CThe function is positive for all , and equals zero when .
  • DThe function is positive at , negative at , and equals zero when .

Q22:

Determine the sign of the function .

  • A The function is positive when , the function is negative when , and the function equals zero when .
  • B The function is positive when , the function is negative when , and the function equals zero when .
  • C The function is positive when , the function is negative when , and the function equals zero when .
  • D The function is positive when , the function is negative when , and the function equals zero when .

Q23:

Determine the interval in which the function is NOT negative.

  • A
  • B
  • C
  • D
  • E

Q24:

Determine the sign of the function 𝑓 ( π‘₯ ) = βˆ’ π‘₯ βˆ’ 2 π‘₯ βˆ’ 7 2 .

  • AThe function is positive for all π‘₯ ∈ ℝ βˆ’ { 0 } , and the function equals zero when π‘₯ = 0 .
  • BThe function is positive for all π‘₯ ∈ ℝ .
  • CThe function is negative for all π‘₯ ∈ ℝ βˆ’ { 0 } , and the function equals zero when π‘₯ = 0 .
  • DThe function is negative for all π‘₯ ∈ ℝ .

Q25:

Determine the sign of the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 1 6 π‘₯ + 6 4 2 .

  • AThe function is positive when π‘₯ ∈ ℝ βˆ’ { βˆ’ 8 , 8 } , and the function equals zero when π‘₯ ∈ { βˆ’ 8 , 8 } .
  • BThe function is positive for all π‘₯ ∈ ℝ .
  • CThe function is positive when π‘₯ ∈ ℝ βˆ’ { βˆ’ 8 } , and the function equals zero when π‘₯ = βˆ’ 8 .
  • DThe function is positive when π‘₯ ∈ ℝ βˆ’ { 8 } , and the function equals zero when π‘₯ = 8 .