INCREASING AND DECREASING FUNCTIONS WORKSHEET

Problem 1 : 

The graph shown below gives the weight W of a person at age x. Determine the intervals on which the function W is increasing and on which it is decreasing.

Problem 2 :

(a)  Sketch the graph of the function f(x) = x^2/3.  

(b)  Find the domain and range of the function.

(c)  Find the intervals on which f increases and decreases.

Problem 3 :

The graph of the function shown below has domain [−1, 6].

(a) Find the largest interval on which f is increasing.

(b) Find the largest interval on which f is decreasing.

(c) Find the largest interval containing 6 on which f is decreasing.

Problem 4 :

Shown below are the graphs of three functions; each function is graphed on its entire domain.

(a) Is f increasing, decreasing, or neither?

(b) Is g increasing, decreasing, or neither?

(c) Is h increasing, decreasing, or neither?

Problem 5 :

Here f has domain [0, 4] and g has domain [−1, 5].

(i)  What is the largest interval contained in the domain of f on which f is increasing?

(ii)  What is the largest interval contained in the domain of g on which g is increasing?

1. Answer :

The function is increasing on [0, 25] and [35, 40]. It is decreasing on [40, 50]. The function is constant (neither increasing nor decreasing) on [25, 35] and [50, 80]. This means that the person gained weight until age 25, then gained weight again between ages 35 and 40. He lost weight between ages 40 and 50.

2. Answer : 

(a)  We can use a graphing calculator to sketch the graph shown below. 

From the graph above, we can observer that

(b)  the domain of f is R and the range is [0, ∞). 

(c)  f is decreasing on (-∞, 0] and increasing on [0, ∞). 

3. Answer :

From the graph above, we can observe,

(a) [1, 5] is the largest interval on which f is increasing.

(b) [−1, 1] is the largest interval on which f is decreasing.

(c) [5, 6] is the largest interval containing 6 on which f is decreasing.

4. Answer :

(a) The graph of f gets lower from left to right on its entire domain. Thus f is decreasing.

(b) The graph of g gets higher from left to right on its entire domain. Thus g is increasing.

(c) The graph of h gets lower from left to right on part of its domain and gets higher from left to right on another part of its domain. Thus h is neither increasing nor decreasing.

5. Answer :

(i) The largest interval on which the function f increasing is [3, 4].

(i) The largest interval on which the function g decreasing is [0, 3].

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