How do you find the average rate of change of #g ( x) =10x −3# over the interval [1,5]?

Question

Elijah Abram · Accepted Answer

The average rate of change is #10#.

Since the graph of this function is a line, the average rate of change is equal to the slope of the line from one endpoint to the other. OR The average rate of change of #f(x)# on #[a,b]# is #(f(b)-f(a))/(b-a)# in this instance, we obtain #(g(5) - g(1)) /(5-4) = (47-7)/4 = 10#

Axel Alvarez · Answer

undefined To find the average rate of change of $ g(x) = 10x - 3 $ over the interval $[1,5]$, you evaluate $ g(5) $ and $ g(1) $, and then calculate the difference in the function values over the difference in the input values. This is expressed as:

$$ \text{Average rate of change} = \frac{g(5) - g(1)}{5 - 1} $$

Isabella Ackerman · Answer

undefined To find the average rate of change of $ g(x) = 10x - 3 $ over the interval $[1, 5]$, you can use the formula for average rate of change:

$$ \text{Average Rate of Change} = \frac{{g(b) - g(a)}}{{b - a}} $$

where $ a $ and $ b $ are the endpoints of the interval. In this case, $ a = 1 $ and $ b = 5 $.

Substitute the values of $ a $, $ b $, and the function $ g(x) $ into the formula:

$$ \text{Average Rate of Change} = \frac{{g(5) - g(1)}}{{5 - 1}} $$

$$ = \frac{{(10(5) - 3) - (10(1) - 3)}}{{5 - 1}} $$

$$ = \frac{{(50 - 3) - (10 - 3)}}{{5 - 1}} $$

$$ = \frac{{(47) - (7)}}{{4}} $$

$$ = \frac{{40}}{{4}} $$

$$ = 10 $$

Therefore, the average rate of change of $ g(x) = 10x - 3 $ over the interval $[1, 5]$ is $ 10 $.