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

Q2:

What condition must there be on for ,where is a positive number, to be an increasing function?

• A
• B
• C
• D

Q3:

The graph of a function is given below. Which of the following statements about the function is true? • AThe function is decreasing on .
• BThe function is constant on .
• CThe function is increasing on .
• DThe function is increasing on .
• EThe function is constant on .

Q4:

Which of the following correctly describes the monotonicity of the function represented by the graph in the figure below? • AThe function is increasing on and constant on .
• BThe function is decreasing on and constant on .
• CThe function is decreasing on and constant on .
• DThe function is increasing on and constant on .

Q5:

Which of the following statements correctly defines the domain and range of the function and accurately describes its monotonicity?

• AThe domain is , the range is , and the function is decreasing over its domain.
• BThe domain is , the range is , and the function is increasing over its domain.
• CThe domain is , the range is , and the function is increasing over its domain.
• DThe domain is , the range is , and the function is decreasing over its domain.
• EThe domain is , the range is , and the function is decreasing over its domain.

Q6:

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 .

Q7:

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

• A
• B
• C
• D

Q8:

Is the function shown increasing, decreasing, or constant in the interval ? • Aincreasing
• Bconstant
• Cdecreasing

Q9:

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 increasing on and increasing on .
• DThe function is decreasing on and decreasing on .

Q10:

Given that , determine the intervals on which is increasing or decreasing.

• AThe function is increasing on the intervals and and decreasing on the interval .
• BThe function is increasing on the intervals and and decreasing on the interval .
• CThe function is increasing on the intervals and and decreasing on the interval .
• DThe function is increasing on the interval and decreasing on the intervals and .
• EThe function is increasing on the interval and decreasing on the intervals and .

Q11:

The graph of a function is given below. Which of the following statements about the function is true? • AThe function is constant on and constant on .
• BThe function is constant on and constant on .
• CThe function is constant on and constant on .
• DThe function is constant on and constant on .

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 on the interval and decreasing on the interval .
• D is increasing on the interval and decreasing on the interval .

Q13:

Which of the following statements is true for the function ?

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

Q14:

Which of the following statements is true for the function ?

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

Q15:

How do the values of the function behave as increases?

• AThe values of increase.
• BThe values of decrease.
• CThe values of are constant.

Q16:

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

Q17:

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 .

Q18:

Which of the following statements correctly describe the monotony of the function represented in the figure below? • AThe function is increasing on , constant on , and decreasing on .
• BThe function is increasing on , constant on , and decreasing on .
• CThe function is increasing on and decreasing on .
• DThe function is increasing on and decreasing on .

Q19:

Which of the following statements is true for the function ?

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

Q20:

Which of the following statements correctly describe the monotony on the domain of the function represented in the figure below? • AThe function is increasing on and decreasing on .
• BThe function is increasing on and decreasing on .
• CThe function is increasing on and decreasing on .
• DThe function is increasing on and decreasing on .

Q21:

The graph of a function is given below. Which of the following statements about the function is true? • AThe function is increasing on and decreasing on .
• BThe function is increasing on and decreasing on .
• CThe function is increasing on and decreasing on .
• DThe function is increasing on and decreasing on .

Q22:

Which of the following statements is true for the function ?

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

Q23:

Discuss the monotonicity of the following function on its domain. • AIncreasing on and decreasing on
• BIncreasing on and decreasing on
• CIncreasing on and decreasing on
• DIncreasing on and decreasing on

Q24:

Which of the following statements is true for the function ?

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

Q25:

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 on the interval and decreasing on the interval .
• D is increasing on the interval and decreasing on the interval .