Choose two ordered pairs from the table of values.
B
b
Find two point pairs from the graph.
C
c
Find two ordered pairs and evaluate the function two times at different x values.
Practice makes perfect
a
Remember that we can calculate the average rate of change of a function between two points as the quotient between the change in the y variable and the change in the x variable. If we have a table of values we can chose two ordered pairs (x_1,y_1),(x_2,y_2) and calculate it as indicated below.
Rate of change &= Change in $y$/Change in $x$
Rate of change &= y_2-y_1/x_2-x_1
Example
y
x
2
1
4
2
6
3
8
4
Rate of change &= 6-2/3-1=2
b
As we discussed in Part A, we can calculate the average rate of change of a function between two points as the quotient between the change in the y variable and the change in the x variable. In a graph we can do this by localizing two points (x_1,y_1),(x_2,y_2) and calculating it as indicated.
Rate of change &= Change in $y$/Change in $x$
Rate of change &= y_2-y_1/x_2-x_1
Example
Rate of change &= Change in $y$/Change in $x$
Rate of change &= 3-/3- = 1
c
Once again, we need to find two ordered pairs (x_1,y_1),(x_2,y_2) for the function, then we can calculate the rate of change as indicated.
Rate of change &= Change in $y$/Change in $x$
Rate of change &= y_2-y_1/x_2-x_1If we have an equation we can evaluate it at two different x values to find the corresponding y values.
Example
Let's consider the function y = 5x +4. When x=1 we have y= 5(1)+4=9. When x=4 we have y= 5(4)+4=24. We can use these values and find the rate of change.
Rate of change &= Change in $y$/Change in $x$
Rate of change &= 24-9/4-1 = 5
