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?

  • A𝑥138
  • B𝑥>138
  • C𝑥>138
  • D𝑥138
  • E𝑥<138

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?

  • A𝑓(𝑥) is positive for 𝑥3.
  • B𝑓(𝑥) is negative for 𝑥3.
  • C𝑓(𝑥) is positive for 𝑥3.
  • D𝑓(𝑥) is positive for 𝑥9.
  • E𝑓(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?

  • A𝑥
  • B𝑥{0}
  • C𝑥<0
  • D𝑥>0

Q16:

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

  • A[20,20]
  • B(,20)
  • C(20,)
  • D(,20)
  • E(20,20)

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?

  • A𝑥>8
  • B𝑥>6
  • C𝑥<8
  • D𝑥<6
  • E𝑥>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,52
  • D,52(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.

  • A𝑓(𝑥) is negative for 𝑥{0}.
  • B𝑓(𝑥) is positive for 𝑥>0.
  • C𝑓(𝑥) is positive for 𝑥{0}.
  • D𝑓(𝑥) is negative for 𝑥.
  • E𝑓(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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