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In this lesson, we will learn how to find the intervals over which a function is increasing, constant, or decreasing.

Q1:

Discuss the monotony of the function , where .

Q2:

What condition must there be on 𝑧 for 𝑓 ( 𝑥 ) = 𝑧 7 𝑥 ,where 𝑥 is a positive number, to be an increasing function?

Q3:

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

Q4:

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

Q5:

Which of the following statements correctly defines the domain and range of the function 𝑓 ( 𝑥 ) = − 5 − 5 𝑥 and accurately describes its monotonicity?

Q6:

Which of the following statements is true for the function 𝑓 ( 𝑥 ) = ( 𝑥 − 1 2 ) 2 ?

Q7:

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

Q8:

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

Q9:

Q10:

Given that 𝑓 ( 𝑥 ) = − 5 𝑥 + ( 𝑥 + 4 ) − 5 5 , determine the intervals on which 𝑓 is increasing or decreasing.

Q11:

Q12:

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

Q13:

Which of the following statements is true for the function ℎ ( 𝑥 ) = − 1 7 − 𝑥 − 5 ?

Q14:

Which of the following statements is true for the function 𝑓 ( 𝑥 ) = 𝑥 − 1 𝑥 − 1 2 ?

Q15:

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

Q16:

Determine the intervals of increase and decrease of the function 𝑓 ( 𝑥 ) = − 7 𝑥 2 given that 𝑥 ∈ ℝ .

Q17:

Which of the following statements is true for the function 𝑓 ( 𝑥 ) = − ( 𝑥 − 1 2 ) 2 ?

Q18:

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

Q19:

Which of the following statements is true for the function 𝑓 ( 𝑥 ) = 1 − 5 − 𝑥 ?

Q20:

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

Q21:

Q22:

Which of the following statements is true for the function 𝑓 ( 𝑥 ) = ( − 𝑥 − 6 ) 3 ?

Q23:

Discuss the monotonicity of the following function on its domain.

Q24:

Which of the following statements is true for the function 𝑓 ( 𝑥 ) = − 1 0 𝑥 3 ?

Q25:

Determine the intervals of increase and decrease of the function 𝑓 ( 𝑥 ) = 𝑥 + 1 0 𝑥 2 given that 𝑥 ∈ [ − 7 , − 1 ] .

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