The average rate of change of g(x) = 2x-1 from x = 2 to x = 6 is 7.5.
true or false
g ( 2 ) = 2 * 2 - 1 = 4 - 1 = 3
g ( 6 ) = 2 * 6 - 1 = 12 - 1 = 11
11 - 3 = 8
6 - 2 = 4
8 / 4 = 2
False
No calculations are necessary.
The function is linear, so the rate of change is constant, namely its slope which is 2
so the average rate of change is 2 , not 7.5
To determine if the statement is true or false, we need to calculate the average rate of change of the function g(x) = 2x - 1 from x = 2 to x = 6.
The average rate of change of a function over an interval is given by the following formula:
Average rate of change = (g(x2) - g(x1)) / (x2 - x1)
where g(x2) represents the value of the function at x = x2, g(x1) represents the value of the function at x = x1, x2 represents the ending point of the interval, and x1 represents the starting point of the interval.
In this case, x1 = 2, x2 = 6, and g(x) = 2x - 1. Let's calculate the average rate of change:
g(6) = 2(6) - 1 = 11
g(2) = 2(2) - 1 = 3
Average rate of change = (g(6) - g(2)) / (6 - 2) = (11 - 3) / 4 = 8 / 4 = 2
The average rate of change of the function g(x) = 2x - 1 from x = 2 to x = 6 is 2, not 7.5.
Therefore, the statement "The average rate of change of g(x) = 2x - 1 from x = 2 to x = 6 is 7.5" is false.