# 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.

**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 .

**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 .

**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 .