Question

Match the graphs according to their nature with the correct functions.

• A. Decreasing function
• B. Constant function
• C. Increasing function

Answer 1

Let us consider the first graph:


Tabulating the above information, we get:

Time (in years)	0	1	2	3	4	5	6
Production (in thousands)	75	62.5	50	38.5	25	12.5	0

Consider any two points, say (0,75) and (2,50).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{50-75}{2-0}=-12.5$

Here, the rate of change (slope) is negative.

It denotes the rate of change is decreasing at a constant rate.

So, the first graph represents a decreasing function.


Let us consider the second graph:


Tabulating the above information, we get:

Time (in years)	0	1	2	3	4	5	6
Production (in thousands)	20	28	36	44	52	60	68

Consider any two points, say (0,20) and (1,28).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{28-20}{1-0}=8$

Here, the rate of change (slope) is positive.

It denotes the rate of change is increasing at a constant rate.

So, the second graph represents an increasing function.

Let us consider the third graph:


Tabulating the above infromation, we get:

Time (in years)	0	1	2	3	4	5	6
Production (in thousands)	40	40	40	40	40	40	40

Consider any two points, say (0,40) and (1,40).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{40-40}{1-0}=0$

Here, the rate of change (slope) is zero.

It denotes the rate of change is constant here.

So, the third graph represents a constant function.