Question

Which of the following functions have an average rate of change equal to 0 on the interval from x=-1 to x=1 ? Select all that apply.

a.f(x)=4
b.f(x)=-4x+1
c.f(x)=4-x(2)
d.f(x)=4x(2)-1

Answer 1

Functions a, b, c, and d all have an average rate of change equal to 0 on the interval from x = -1 to x = 1.

Step-by-step explanation:

The average rate of change of a function on an interval [a, b] is computed using the formula (f(b) - f(a)) / (b - a). For the interval from x = -1 to x = 1, this formula reduces to (f(1) - f(-1)) / 2.

1. f(x) = 4 is a constant function, and its average rate of change is (4 - 4) / 2 = 0.
2. f(x) = -4x + 1 is a linear function, and its average rate of change is ((-4(1) + 1) - (-4(-1) + 1)) / 2, which simplifies to (-3 - (-3)) / 2 = 0.
3. f(x) = 4 - x2 is a quadratic function, and its average rate of change is ((4 - 12) - (4 - (-1)2)) / 2 = (3 - 3) / 2 = 0.
4. f(x) = 4x2 - 1 is also a quadratic function, but its average rate of change is ((4(1)2 - 1) - (4(-1)2 - 1)) / 2 = (3 - 3) / 2 = 0.

Therefore, functions a, b, c, and d all have an average rate of change equal to 0 on the interval from x = -1 to x = 1.