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

Lesson: Increasing and Decreasing Intervals of a Function

Sample Question Videos

Worksheet • 25 Questions • 2 Videos

Q1:

Discuss the monotony of the function , where .

  • A is decreasing on the interval .
  • B is increasing on the interval .
  • C is increasing on the interval .
  • D is decreasing on the interval and increasing on the interval .
  • E is increasing on the interval and decreasing on the interval .

Q2:

What condition must there be on 𝑧 for 𝑓 ( π‘₯ ) = ο€» 𝑧 7  π‘₯ ,where π‘₯ is a positive number, to be an increasing function?

  • A 𝑧 > 7
  • B 𝑧 > 1
  • C 𝑧 < 7
  • D 𝑧 > 0

Q3:

The graph of a function is given below. Which of the following statements about the function is true?

  • A The function is constant on ℝ .
  • B The function is increasing on ] βˆ’ ∞ , 0 ] .
  • C The function is increasing on ℝ .
  • D The function is constant on ] βˆ’ ∞ , 0 ] .
  • E The function is decreasing on ℝ .

Q4:

Which of the following correctly describes the monotonicity of the function represented by the graph in the figure below?

  • A The function is decreasing on ] 9 , ∞ [ and constant on ] βˆ’ ∞ , 9 [ .
  • B The function is decreasing on ] βˆ’ ∞ , βˆ’ 2 [ and constant on ] βˆ’ 2 , ∞ [ .
  • C The function is increasing on ] βˆ’ ∞ , βˆ’ 2 [ and constant on ] βˆ’ 2 , ∞ [ .
  • D The function is increasing on ] 9 , ∞ [ and constant on ] βˆ’ ∞ , 9 [ .

Q5:

Which of the following statements correctly defines the domain and range of the function 𝑓 ( π‘₯ ) = βˆ’ 5 βˆ’ 5 π‘₯ and accurately describes its monotonicity?

  • A The domain is ℝ , the range is ℝ , and the function is decreasing over its domain.
  • B The domain is ℝ βˆ’ { βˆ’ 1 , βˆ’ 5 } , the range is { βˆ’ 1 , βˆ’ 5 } , and the function is decreasing over its domain.
  • C The domain is ℝ , the range is ℝ , and the function is increasing over its domain.
  • D The domain is ℝ βˆ’ { βˆ’ 1 } , the range is { βˆ’ 1 } , and the function is increasing over its domain.
  • E The domain is ℝ βˆ’ { βˆ’ 1 } , the range is { βˆ’ 1 } , and the function is decreasing over its domain.

Q6:

Which of the following statements is true for the function 𝑓 ( π‘₯ ) = ( π‘₯ βˆ’ 1 2 ) 2 ?

  • A 𝑓 ( π‘₯ ) is increasing on ] 1 2 , ∞ [ and decreasing on ] βˆ’ ∞ , 1 2 [ .
  • B 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 1 2 [ and decreasing on ] 1 2 , ∞ [ .
  • C 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , βˆ’ 1 2 [ and decreasing on ] βˆ’ 1 2 , ∞ [ .
  • D 𝑓 ( π‘₯ ) is increasing on ] βˆ’ 1 2 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 1 2 [ .

Q7:

A particle is moving in a straight line such that its velocity 𝑣 after 𝑑 seconds is given by When is the velocity of the particle increasing?

  • A 𝑑 < 3 4 s
  • B 𝑑 > 3 4 s
  • C 𝑑 > 6 8 s
  • D 𝑑 < 6 8 s

Q8:

Is the function shown increasing, decreasing, or constant in the interval ( βˆ’ 2 , 2 ) ?

  • Aincreasing
  • Bdecreasing
  • Cconstant

Q9:

The graph of a function is given below. Which of the following statements about the function is true?

  • AThe function is increasing on ] βˆ’ ∞ , 0 [ and increasing on ] 0 , ∞ [ .
  • BThe function is decreasing on ] βˆ’ ∞ , 0 [ and decreasing on ] 0 , ∞ [ .
  • CThe function is decreasing on ] βˆ’ ∞ , βˆ’ 5 [ and decreasing on ] βˆ’ 5 , ∞ [ .
  • DThe function is increasing on ] βˆ’ ∞ , βˆ’ 5 [ and increasing on ] βˆ’ 5 , ∞ [ .

Q10:

Given that 𝑓 ( π‘₯ ) = βˆ’ 5 π‘₯ + ( π‘₯ + 4 ) βˆ’ 5 5 , determine the intervals on which 𝑓 is increasing or decreasing.

  • A The function is increasing on the intervals ] βˆ’ ∞ , βˆ’ 5 [ and ] βˆ’ 3 , ∞ [ and decreasing on the interval ] βˆ’ 5 , βˆ’ 3 [ .
  • BThe function is increasing on the intervals ] βˆ’ 5 , βˆ’ 3 [ and ] βˆ’ 3 , ∞ [ and decreasing on the interval ] βˆ’ ∞ , βˆ’ 3 [ .
  • CThe function is increasing on the interval ] βˆ’ 5 , βˆ’ 3 [ and decreasing on the intervals ] βˆ’ ∞ , βˆ’ 5 [ and ] βˆ’ 3 , ∞ [ .
  • DThe function is increasing on the interval ] βˆ’ 3 , ∞ [ and decreasing on the intervals ] βˆ’ ∞ , βˆ’ 5 [ and ] βˆ’ 5 , βˆ’ 3 [ .
  • EThe function is increasing on the intervals ] βˆ’ ∞ , βˆ’ 5 [ and ] βˆ’ 5 , βˆ’ 3 [ and decreasing on the interval ] βˆ’ 3 , ∞ [ .

Q11:

The graph of a function is given below. Which of the following statements about the function is true?

  • A The function is constant on ] βˆ’ ∞ , 0 ] and constant on ] 0 , ∞ [ .
  • B The function is constant on ] βˆ’ ∞ , 1 ] and constant on [ βˆ’ 1 , ∞ [ .
  • C The function is constant on ] βˆ’ ∞ , 1 ] and constant on ] 0 , ∞ [ .
  • D The function is constant on ] βˆ’ ∞ , 0 ] and constant on [ βˆ’ 1 , ∞ [ .

Q12:

Determine the intervals of increase and decrease of the function 𝑓 ( π‘₯ ) = βˆ’ π‘₯ βˆ’ 8 π‘₯ 2 given that π‘₯ ∈ ] βˆ’ 8 , βˆ’ 1 [ .

  • A 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 8 , βˆ’ 4 [ and decreasing on the interval ] βˆ’ 4 , βˆ’ 1 [ .
  • B 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 4 , βˆ’ 1 [ and decreasing on the interval ] βˆ’ 8 , βˆ’ 4 [ .
  • C 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 4 , ∞ [ and decreasing on the interval ] βˆ’ ∞ , βˆ’ 4 [ .
  • D 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ ∞ , βˆ’ 4 [ and decreasing on the interval ] βˆ’ 4 , ∞ [ .

Q13:

Which of the following statements is true for the function β„Ž ( π‘₯ ) = βˆ’ 1 7 βˆ’ π‘₯ βˆ’ 5 ?

  • A β„Ž ( π‘₯ ) is decreasing on the intervals ] βˆ’ ∞ , 7 [ and ] 7 , ∞ [ .
  • B β„Ž ( π‘₯ ) is increasing on the intervals ] βˆ’ ∞ , 7 [ and ] 7 , ∞ [ .
  • C β„Ž ( π‘₯ ) is increasing on the intervals ] βˆ’ ∞ , βˆ’ 7 [ and ] βˆ’ 7 , ∞ [ .
  • D β„Ž ( π‘₯ ) is decreasing on the intervals ] βˆ’ ∞ , βˆ’ 7 [ and ] βˆ’ 7 , ∞ [ .

Q14:

Which of the following statements is true for the function 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 1 π‘₯ βˆ’ 1 2 ?

  • A 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 1 [ and ] 1 , ∞ [ .
  • B 𝑓 ( π‘₯ ) is increasing on ] 1 , ∞ [ and decreasing on ] βˆ’ ∞ , 1 [ .
  • C 𝑓 ( π‘₯ ) is decreasing on ] βˆ’ ∞ , 1 [ and ] 1 , ∞ [ .
  • D 𝑓 ( π‘₯ ) is decreasing on ℝ .
  • E 𝑓 ( π‘₯ ) is increasing on ℝ .

Q15:

How do the values of the function 𝑓 ( π‘₯ ) = πœ‹ βˆ’ 3 π‘₯ behave as π‘₯ increases?

  • AThe values of 𝑓 ( π‘₯ ) increase.
  • BThe values of 𝑓 ( π‘₯ ) decrease.
  • CThe values of 𝑓 ( π‘₯ ) are constant.

Q16:

Determine the intervals of increase and decrease of the function 𝑓 ( π‘₯ ) = βˆ’ 7 π‘₯ 2 given that π‘₯ ∈ ℝ .

  • A 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ ∞ , 0 [ and decreasing on the interval ] 0 , ∞ [ .
  • B 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 7 , ∞ [ and decreasing on the interval ] βˆ’ ∞ , βˆ’ 7 [ .
  • C 𝑓 ( π‘₯ ) is increasing on the interval ] 0 , ∞ [ and decreasing on the interval ] βˆ’ ∞ , 0 [ .
  • D 𝑓 ( π‘₯ ) is increasing everywhere.
  • E 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ ∞ , βˆ’ 7 [ and decreasing on the interval ] βˆ’ 7 , ∞ [ .

Q17:

Which of the following statements is true for the function 𝑓 ( π‘₯ ) = βˆ’ ( π‘₯ βˆ’ 1 2 ) 2 ?

  • A 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 1 2 [ and decreasing on ] 1 2 , ∞ [ .
  • B 𝑓 ( π‘₯ ) is increasing on ] 1 2 , ∞ [ and decreasing on ] βˆ’ ∞ , 1 2 [ .
  • C 𝑓 ( π‘₯ ) is increasing on ] βˆ’ 1 2 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 1 2 [ .
  • D 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , βˆ’ 1 2 [ and decreasing on ] βˆ’ 1 2 , ∞ [ .

Q18:

Which of the following statements correctly describe the monotony of the function represented in the figure below?

  • A The function is increasing on ] βˆ’ 2 , βˆ’ 1 [ , constant on ] βˆ’ 1 , 5 [ , and decreasing on ] 5 , 8 [ .
  • B The function is increasing on ] 5 , 8 [ , constant on ] βˆ’ 1 , 5 [ , and decreasing on ] βˆ’ 2 , βˆ’ 1 [ .
  • C The function is increasing on ] 5 , 8 [ and decreasing on ] βˆ’ 2 , 5 [ .
  • D The function is increasing on ] βˆ’ 2 , 5 [ and decreasing on ] 5 , 8 [ .

Q19:

Which of the following statements is true for the function 𝑓 ( π‘₯ ) = 1 βˆ’ 5 βˆ’ π‘₯ ?

  • A 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , βˆ’ 5 [ and increasing on ] βˆ’ 5 , ∞ [ .
  • B 𝑓 ( π‘₯ ) is decreasing on ] βˆ’ ∞ , βˆ’ 5 [ and decreasing on ] βˆ’ 5 , ∞ [ .
  • C 𝑓 ( π‘₯ ) is decreasing on ] βˆ’ ∞ , 5 [ and decreasing on ] 5 , ∞ [ .
  • D 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 5 [ and increasing on ] 5 , ∞ [ .

Q20:

Which of the following statements correctly describe the monotony on the domain of the function represented in the figure below?

  • A The function is increasing on ] βˆ’ 2 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 2 [ .
  • B The function is increasing on ] βˆ’ ∞ , βˆ’ 1 [ and decreasing on ] βˆ’ 1 , ∞ [ .
  • C The function is increasing on ] βˆ’ 1 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 1 [ .
  • D The function is increasing on ] βˆ’ ∞ , βˆ’ 2 [ and decreasing on ] βˆ’ 2 , ∞ [ .

Q21:

The graph of a function is given below. Which of the following statements about the function is true?

  • AThe function is increasing on ] 2 , ∞ [ and decreasing on ] βˆ’ ∞ , 2 [ .
  • BThe function is increasing on ] βˆ’ ∞ , 2 [ and decreasing on ] 2 , ∞ [ .
  • CThe function is increasing on ] βˆ’ 1 , ∞ [ and decreasing on ] βˆ’ ∞ , 3 [ .
  • DThe function is increasing on ] βˆ’ ∞ , 3 [ and decreasing on ] βˆ’ 1 , ∞ [ .

Q22:

Which of the following statements is true for the function 𝑓 ( π‘₯ ) = ( βˆ’ π‘₯ βˆ’ 6 ) 3 ?

  • A 𝑓 ( π‘₯ ) is decreasing on ℝ .
  • B 𝑓 ( π‘₯ ) is increasing on ℝ .
  • C 𝑓 ( π‘₯ ) is increasing on ] βˆ’ 6 , ∞ [ and decreasing on ] βˆ’ ∞ , βˆ’ 6 [ .
  • D 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , βˆ’ 6 [ and decreasing on ] βˆ’ 6 , ∞ [ .

Q23:

Discuss the monotonicity of the following function on its domain.

  • Aincreasing on ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ ( 1 , 4 ) and decreasing on ( βˆ’ 2 , 1 ) βˆͺ ( 4 , ∞ )
  • Bincreasing on ( βˆ’ 2 , 1 ) βˆͺ ( 4 , ∞ ) and decreasing on ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ ( 1 , 4 )
  • Cincreasing on ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ ( βˆ’ 2 , 1 ) and decreasing on ( 1 , 4 ) βˆͺ ( 4 , ∞ )
  • Dincreasing on ( 1 , 4 ) βˆͺ ( 4 , ∞ ) and decreasing on ( βˆ’ ∞ , βˆ’ 2 ) βˆͺ ( βˆ’ 2 , 1 )

Q24:

Which of the following statements is true for the function 𝑓 ( π‘₯ ) = βˆ’ 1 0 π‘₯ 3 ?

  • A 𝑓 ( π‘₯ ) is decreasing on ℝ .
  • B 𝑓 ( π‘₯ ) is increasing on ] 0 , ∞ [ and decreasing on ] βˆ’ ∞ , 0 [ .
  • C 𝑓 ( π‘₯ ) is increasing on ℝ .
  • D 𝑓 ( π‘₯ ) is increasing on ] βˆ’ ∞ , 0 [ and decreasing on ] 0 , ∞ [ .

Q25:

Determine the intervals of increase and decrease of the function 𝑓 ( π‘₯ ) = π‘₯ + 1 0 π‘₯ 2 given that π‘₯ ∈ [ βˆ’ 7 , βˆ’ 1 ] .

  • A 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 5 , βˆ’ 1 [ and decreasing on the interval ] βˆ’ 7 , βˆ’ 5 [ .
  • B 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 7 , βˆ’ 5 [ and decreasing on the interval ] βˆ’ 5 , βˆ’ 1 [ .
  • C 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ ∞ , βˆ’ 5 [ and decreasing on the interval ] βˆ’ 5 , ∞ [ .
  • D 𝑓 ( π‘₯ ) is increasing on the interval ] βˆ’ 5 , ∞ [ and decreasing on the interval ] βˆ’ ∞ , βˆ’ 5 [ .
Preview