The average rate of change of the function from x = -2 to x = 2 is -1/2, option 3.
How to calculate average rate of change of a function
The average rate of change of a linear function f(x) between two points (x₁) and (x₂) is given by the formula.
Average Rate of Change = f(x₂) - f(x₁)/x₂ - x₁
Given
x₂ = 2, x₁ = -2
Let's find the function using points (3,0) and (-3,3)
slope of line = y₂ - y₁/x₂ - x₁
m = 3 - 0/-3 -3
m = 3/-6 = -1/2
using point (-3,3)
y -3 = -1/2(x + 3)
y = -x/2 - 3/2 +3
y = -x/2 + 3/2
f(x) = -x/2 + 3/2
Evaluate the given values of x
when
x = 2,
f(2) = -2/2 + 3/2
f(2) = -1 + 3/2 = 1/2
when x = -2
f(-2) = 2/2 + 3/2
= 1 + 3/2
= 5/2
Average Rate of Change = f(x₂) - f(x₁)/x₂ - x₁
= (1/2 - 5/2)/2-(-2)
=(-4/2)/4
= -2/4 = -1/2
The negative sign indicates negative slope.
Therefore, the average rate of change of the function from x = -2 to x = 2 is -1/2, option 3.