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Worksheet: Increasing and Decreasing Intervals of a Function

In this worksheet, we will practice finding the intervals over which a function is increasing, constant, or decreasing.

Q1:

Which of the following is true of the function , where .

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

Q2:

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

  • A The function is constant on and constant on .
  • B The function is constant on and constant on .
  • C The function is constant on and constant on .
  • D The function is constant on and constant on .

Q3:

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

  • AThe function is increasing on and increasing on .
  • BThe function is decreasing on and decreasing on .
  • CThe function is decreasing on and decreasing on .
  • DThe function is increasing on and increasing on .

Q4:

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

  • AThe function is increasing on and increasing on .
  • BThe function is decreasing on and decreasing on .
  • CThe function is decreasing on and decreasing on .
  • DThe function is increasing on and increasing on .

Q5:

Determine the intervals of increase and decrease of the function 𝑓 ( 𝑥 ) = − 𝑥 − 8 𝑥 2 given that 𝑥 ∈ ( − 8 , − 1 ) .

  • A 𝑓 ( 𝑥 ) is increasing on the interval ( − ∞ , − 4 ) and decreasing on the interval ( − 4 , ∞ ) .
  • B 𝑓 ( 𝑥 ) is increasing on the interval ( − 4 , − 1 ) and decreasing on the interval ( − 8 , − 4 ) .
  • C 𝑓 ( 𝑥 ) is increasing on the interval ( − 4 , ∞ ) and decreasing on the interval ( − ∞ , − 4 ) .
  • D 𝑓 ( 𝑥 ) is increasing on the interval ( − 8 , − 4 ) and decreasing on the interval ( − 4 , − 1 ) .

Q6:

Which of the following statements is true for the function ?

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

Q7:

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

  • A The function is decreasing on .
  • B The function is increasing on .
  • C The function is constant on .
  • D The function is constant on .
  • E The function is increasing on .

Q8:

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

  • A The function is constant on .
  • B The function is decreasing on .
  • C The function is increasing on .
  • D The function is increasing on .
  • E The function is decreasing on .

Q9:

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

  • A The function is increasing on and constant on .
  • B The function is decreasing on and constant on .
  • C The function is increasing on and constant on .
  • D The function is decreasing on and constant on .

Q10:

Which of the following statements is true for the function ?

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

Q11:

How do the values of the function 𝑓 ( 𝑥 ) = 𝜋 − 3 𝑥 behave as 𝑥 increases?

  • AThe values of 𝑓 ( 𝑥 ) are constant.
  • BThe values of 𝑓 ( 𝑥 ) increase.
  • CThe values of 𝑓 ( 𝑥 ) decrease.

Q12:

Determine the intervals of increase and decrease of the function given that .

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

Q13:

Which of the following statements is true for the function ?

  • A is increasing on and decreasing on .
  • B is increasing on and decreasing on .
  • C is increasing on and decreasing on .
  • D is increasing on and decreasing on .

Q14:

Which of the following statements is true for the function ?

  • A is increasing on and decreasing on .
  • B is increasing on and decreasing on .
  • C is increasing on and decreasing on .
  • D is increasing on and decreasing on .

Q15:

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