Worksheet: Determining the Sign of a Function from a Graph

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

Q1:

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

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

Q2:

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

  • AThe function is positive when 𝑥 { 4 , 2 } and equals zero when 𝑥 { 4 , 2 } .
  • BThe function is positive when 𝑥 ] 4 , 2 [ , negative when 𝑥 [ 4 , 2 ] , and zero when 𝑥 { 4 , 2 } .
  • CThe function is negative when 𝑥 { 4 , 2 } and equals zero when 𝑥 { 4 , 2 } .
  • DThe function is negative when 𝑥 ] 4 , 2 [ , positive when 𝑥 [ 4 , 2 ] , and zero when 𝑥 { 4 , 2 } .

Q3:

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

  • AThe function is negative for all 𝑥 { 1 , 7 } , and the function equals zero when 𝑥 { 1 , 7 } .
  • BThe function is positive when 𝑥 ( 1 , 7 ) , the function is negative when 𝑥 ( 7 , 8 ] , and the function equals zero when 𝑥 { 1 , 7 } .
  • CThe function is positive for all 𝑥 { 1 , 7 } , and the function equals zero when 𝑥 { 1 , 7 } .
  • DThe function is negative when 𝑥 ( 1 , 7 ) , the function is positive when 𝑥 ( 7 , 8 ] , and the function equals zero when 𝑥 { 1 , 7 } .

Q4:

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 }

Q5:

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

  • AThe function is positive when 𝑥 [ 5 , 1 ] , negative when 𝑥 [ 5 , 1 ] , and zero when 𝑥 { 5 , 1 } .
  • BThe function is positive when 𝑥 [ 5 , 1 ] , negative when 𝑥 ] 5 , 1 [ , and zero when 𝑥 { 5 , 1 } .
  • CThe function is positive when 𝑥 [ 5 , 1 ] , negative when 𝑥 [ 5 , 1 ] , and zero when 𝑥 { 5 , 1 } .
  • DThe function is positive when 𝑥 ] 5 , 1 [ , negative when 𝑥 [ 5 , 1 ] , and zero when 𝑥 { 5 , 1 } .
  • EThe function is positive when 𝑥 ] 5 , 1 [ , negative when 𝑥 [ 5 , 1 ] , and zero when 𝑥 { 1 , 5 } .

Q6:

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

  • AThe function is negative for all 𝑥 { 4 } , and zero when 𝑥 = 4 .
  • BThe function is negative for all 𝑥 .
  • CThe function is positive for all 𝑥 { 4 } , and zero when 𝑥 = 4 .
  • DThe function is positive for all 𝑥 .
  • EThe function is positive for all 𝑥 { 6 } , and zero when 𝑥 = 6 .

Q7:

Determine the sign of the function

  • AThe function is negative in the interval { 1 0 } , and the function equals zero at 𝑥 = 1 0 .
  • BThe function is negative in the interval { 1 0 } , and the function equals zero at 𝑥 = 1 0 .
  • CThe function is positive in the interval ] , 1 0 [ , the function is negative in the interval ] 1 0 , [ , and the function equals zero at 𝑥 = 1 0 .
  • DThe function is positive in the interval { 1 0 } , and the function equals zero at 𝑥 = 1 0 .

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