Worksheet: Sign of a Function

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

Q1:

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

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

Q2:

For which values of 𝑥 is the function 𝑓(𝑥)=8𝑥13 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 for all 𝑥.
  • BThe function is positive when 𝑥{0}, and equals zero when 𝑥=0.
  • 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.

Q4:

Determine the sign of the function 𝑓(𝑥)=15𝑥 in .

  • AThe function is positive when 𝑥<0, negative when 𝑥>0, and equals zero when 𝑥=0.
  • BThe function is negative for all 𝑥.
  • CThe function is positive for all 𝑥.
  • 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)=5𝑥+5.

  • AThe function is positive when 𝑥>1, the function is negative when 𝑥<1, and the function equals zero when 𝑥=1.
  • BThe function is positive when 𝑥<1, the function is negative when 𝑥>1, and the function equals zero when 𝑥=1.
  • CThe function is positive when 𝑥<1, the function is negative when 𝑥>1, and the function equals zero when 𝑥=1.
  • Dpositive
  • EThe function is positive when 𝑥>1, the function is negative when 𝑥<1, and the function equals zero when 𝑥=1.

Q6:

Determine the sign of the function 𝑓(𝑥)=517𝑥.

  • AThe function is negative when 𝑥<35, positive when 𝑥>35, and zero when 𝑥=35.
  • BThe function is positive when 𝑥{5}, and zero when 𝑥=5.
  • CThe function is positive when 𝑥<35, negative when 𝑥>35, and zero when 𝑥=35.
  • DThe function is negative when 𝑥<5, positive when 𝑥>5, and zero when 𝑥=5.
  • EThe function is positive when 𝑥<35, negative when 𝑥>35, and zero when 𝑥=35.

Q7:

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

  • A 𝑓 ( 𝑥 ) is positive for 𝑥3.
  • B 𝑓 ( 𝑥 ) is negative for 𝑥3.
  • C 𝑓 ( 𝑥 ) is positive for 𝑥3.
  • D 𝑓 ( 𝑥 ) is positive for 𝑥9.
  • E 𝑓 ( 𝑥 ) is negative for 𝑥3.

Q8:

Determine the sign of the function 𝑓(𝑥)=(𝑥8)(𝑥7).

  • AThe function is positive when 𝑥[7,8], the function is negative when 𝑥(7,8), and the function equals zero when 𝑥{7,8}.
  • BThe function is positive when 𝑥{7,8}, the function is negative when 𝑥[7,8], and the function equals zero when 𝑥{7,8}.
  • CThe function is positive when 𝑥[7,8], the function is negative when 𝑥{7,8}, and the function equals zero when 𝑥{7,8}.
  • DThe 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)=(𝑥1)(𝑥+6) is positive in which interval?

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

Q10:

Determine the sign of the function 𝑓(𝑥)=425𝑥.

  • AThe function is positive for all 𝑥25, and equals zero when 𝑥=25.
  • BThe function is positive for all 𝑥{2}, and equals zero when 𝑥=2.
  • CThe function is negative at 𝑥25,25, positive at 𝑥25,25, and equals zero when 𝑥25,25.
  • DThe function is positive at 𝑥25,25, negative at 𝑥25,25, and equals zero when 𝑥25,25.

Q11:

Determine the sign of the function 𝑓(𝑥)=𝑥+10𝑥+16.

  • AThe function is positive when 𝑥(8,2), the function is negative when 𝑥[8,2], and the function equals zero when 𝑥{8,2}.
  • BThe function is positive when 𝑥[8,2], the function is negative when 𝑥(8,2), and the function equals zero when 𝑥{8,2}.
  • CThe function is positive when 𝑥{8,2}, the function is negative when 𝑥[8,2], and the function equals zero when 𝑥{8,2}.
  • DThe 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)=𝑥16𝑥+64.

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

Q13:

Determine the sign of the function 𝑓(𝑥)=𝑥2𝑥7.

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

Q14:

Determine the sign of the function 𝑓(𝑥)=7𝑥+167𝑥+64 in .

  • AThe function is positive when 𝑥78 and is zero when 𝑥=78.
  • BThe function is negative when 𝑥87 and is zero when 𝑥=87.
  • CThe function is positive when 𝑥87 and is zero when 𝑥=87.
  • DThe function is negative when 𝑥87 and is zero when 𝑥=87.
  • EThe function is positive when 𝑥87 and is zero when 𝑥=87.

Q15:

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

  • A 𝑥
  • B 𝑥 { 0 }
  • C 𝑥 < 0
  • D 𝑥 > 0

Q16:

Determine where the function 𝑓(𝑥)=𝑥400 is positive.

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

Q17:

Determine the interval in which the function 𝑓(𝑥)=158𝑥𝑥 is NOT negative.

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

Q18:

What are the values of 𝑥 for which the functions 𝑓(𝑥)=𝑥5 and 𝑔(𝑥)=𝑥+2𝑥48 are both positive?

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

Q19:

Determine the interval where the sign of each of the two functions 𝑓(𝑥)=2𝑥7𝑥30 and 𝑔(𝑥)=𝑥3𝑥10 are negative together on 𝑅.

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

Q20:

Is there an interval in where the two functions 𝑓(𝑥)=3𝑥+26𝑥40 and 𝑔(𝑥)=96+4𝑥𝑥 are both negative?

  • Ano
  • Byes

Q21:

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

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

Q22:

Determine the sign of the function 𝑓[11,12], where 𝑓(𝑥)=8𝑥.

  • AThe function is positive in the interval (,8), negative in the interval (8,], and equals zero at 𝑥=8.
  • BThe function is positive in the interval [11,8), negative in the interval (8,12], 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 negative in the interval [11,8), positive in the interval (8,12], and equals zero at 𝑥=8.
  • EThe function is positive in the interval [11,8], negative in the interval [8,12], and equals zero at 𝑥=8.

Q23:

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

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

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

Q25:

Determine the sign of the function 𝑓(𝑥)=𝑥+(𝑥2)(6𝑥+3)+2(𝑥+2)+2 in .

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

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