Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Determining the Sign of a Function from a Graph

Sample Question Videos

Worksheet • 7 Questions • 1 Video

Q1:

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

  • AThe function is positive when π‘₯ ∈ ] βˆ’ 1 , 3 [ , the function is negative when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 1 , 3 ] , and the function equals zero when π‘₯ ∈ { βˆ’ 1 , 3 } .
  • BThe function is negative when π‘₯ ∈ ℝ βˆ’ { βˆ’ 1 , 3 } , and the function equals zero when π‘₯ ∈ { βˆ’ 1 , 3 } .
  • CThe function is negative when π‘₯ ∈ ] βˆ’ 1 , 3 [ , the function is positive when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 1 , 3 ] , and the function equals zero when π‘₯ ∈ { βˆ’ 1 , 3 } .
  • DThe function is positive when π‘₯ ∈ ℝ βˆ’ { βˆ’ 1 , 3 } , and the function equals zero when π‘₯ ∈ { βˆ’ 1 , 3 } .
  • EThe function is negative for all π‘₯ ∈ ℝ .

Q2:

Determine the sign of the function represented by the figure below across its domain in ℝ .

  • AThe function is negative when π‘₯ ∈ ] βˆ’ 4 , 2 [ , positive when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 4 , 2 ] , and zero when π‘₯ ∈ { βˆ’ 4 , 2 } .
  • BThe function is positive when π‘₯ ∈ ] βˆ’ 4 , 2 [ , negative when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 4 , 2 ] , and zero when π‘₯ ∈ { βˆ’ 4 , 2 } .
  • CThe function is negative when π‘₯ ∈ ℝ βˆ’ { βˆ’ 4 , 2 } and equals zero when π‘₯ ∈ { βˆ’ 4 , 2 } .
  • DThe function is positive when π‘₯ ∈ ℝ βˆ’ { βˆ’ 4 , 2 } and equals zero when π‘₯ ∈ { βˆ’ 4 , 2 } .

Q3:

Determine the sign of the function represented by the figure below over the interval [ 1 , 8 ] .

  • AThe function is negative when π‘₯ ∈ ( 1 , 7 ) , the function is positive when π‘₯ ∈ ( 7 , 8 ] , and the function equals zero when π‘₯ ∈ { 1 , 7 } .
  • BThe function is positive when π‘₯ ∈ ( 1 , 7 ) , the function is negative when π‘₯ ∈ ( 7 , 8 ] , and the function equals zero when π‘₯ ∈ { 1 , 7 } .
  • CThe function is positive for all π‘₯ ∈ ℝ βˆ’ { 1 , 7 } , and the function equals zero when π‘₯ ∈ { 1 , 7 } .
  • DThe function is negative for all π‘₯ ∈ ℝ βˆ’ { 1 , 7 } , and the function equals zero when π‘₯ ∈ { 1 , 7 } .

Q4:

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

  • A ] 2 , ∞ [
  • B ℝ βˆ’ { βˆ’ 2 }
  • C ] βˆ’ ∞ , βˆ’ 2 [
  • D ] βˆ’ 2 , ∞ [
  • E ] βˆ’ ∞ , 2 [

Q5:

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

  • AThe function is positive when π‘₯ ∈ ] βˆ’ 5 , 1 [ , negative when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 5 , 1 ] , and zero when π‘₯ ∈ { βˆ’ 5 , 1 } .
  • BThe function is positive when π‘₯ ∈ ] βˆ’ 5 , 1 [ , negative when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 5 , 1 ] , and zero when π‘₯ ∈ { βˆ’ 1 , 5 } .
  • CThe function is positive when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 5 , 1 ] , negative when π‘₯ ∈ ] βˆ’ 5 , 1 [ , and zero when π‘₯ ∈ { βˆ’ 5 , 1 } .
  • DThe function is positive when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 5 , 1 ] , negative when π‘₯ ∈ [ βˆ’ 5 , 1 ] , and zero when π‘₯ ∈ { βˆ’ 5 , 1 } .
  • EThe function is positive when π‘₯ ∈ [ βˆ’ 5 , 1 ] , negative when π‘₯ ∈ ℝ βˆ’ [ βˆ’ 5 , 1 ] , and zero when π‘₯ ∈ { βˆ’ 5 , 1 } .

Q6:

Determine the sign of the quadratic function represented in the graph below in ℝ .

  • AThe function is positive for all π‘₯ ∈ ℝ .
  • BThe function is is positive for all π‘₯ ∈ ℝ βˆ’ { 6 } , and zero when π‘₯ = 6 .
  • CThe function is negative for all π‘₯ ∈ ℝ .
  • DThe function is positive for all π‘₯ ∈ ℝ βˆ’ { βˆ’ 4 } , and zero when π‘₯ = βˆ’ 4 .
  • EThe function is negative for all π‘₯ ∈ ℝ βˆ’ { βˆ’ 4 } , and zero when π‘₯ = βˆ’ 4 .

Q7:

Determine the sign of the function

  • AThe function is positive in the interval ℝ βˆ’ { βˆ’ 1 0 } , and the function equals zero at π‘₯ = βˆ’ 1 0 .
  • BThe function is negative in the interval ℝ βˆ’ { βˆ’ 1 0 } , and the function equals zero at π‘₯ = βˆ’ 1 0 .
  • CThe function is positive in the interval ] βˆ’ ∞ , βˆ’ 1 0 [ , the function is negative in the interval ] βˆ’ 1 0 , ∞ [ , and the function equals zero at π‘₯ = βˆ’ 1 0 .
  • DThe function is negative in the interval ℝ βˆ’ { 1 0 } , and the function equals zero at π‘₯ = 1 0 .
Preview