Lesson Worksheet: Sign of a Function Mathematics

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

Q1:

Which of the following correctly describes the interval over which the illustrated function is negative?

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

Q2:

Determine the sign of the function represented by the figure below in .

  • AThe function is negative when 𝑥{1,3}, and the function equals zero when 𝑥{1,3}.
  • BThe function is positive when 𝑥{1,3}, and the function equals zero when 𝑥{1,3}.
  • CThe function is positive when 𝑥(1,3), the function is negative when 𝑥[1,3], and the function equals zero when 𝑥{1,3}.
  • DThe function is negative when 𝑥(1,3), the function is positive when 𝑥[1,3], and the function equals zero when 𝑥{1,3}.
  • EThe function is negative for all 𝑥.

Q3:

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

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

Q4:

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.

Q5:

For which values of 𝑥 is the function 𝑓(𝑥)=8𝑥13 positive?

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

Q6:

Determine the sign of the function 𝑓(𝑥)=(2𝑥1).

  • AThe function is negative when 𝑥12 and equals zero when 𝑥=12.
  • BThe function is positive when 𝑥12 and equals zero when 𝑥=12.
  • CThe function is positive when 𝑥{2} and equals zero when 𝑥=2.
  • DThe function is negative for all 𝑥.
  • EThe function is positive when 𝑥{1} and equals zero when 𝑥=1.

Q7:

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}.

Q8:

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.

Q9:

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

Q10:

Determine the interval where the sign of both of the two functions 𝑓(𝑥)=2𝑥7𝑥30 and 𝑔(𝑥)=𝑥3𝑥10 is negative in 𝑅.

  • A(6,)
  • B[2,5]
  • C,52
  • D,52(6,)
  • E(2,5)

This lesson includes 38 additional questions and 369 additional question variations for subscribers.

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