Question

Let e f (x) = x2 – 2x - 4 What is the average rate of change for the quadratic function from X = -1 tox to x = 42 Enter your answer in the box.​

Answer 1

Answer:

The average rate of change of the given function

A(x) =  1

Step-by-step explanation:

Step(i):-

Given function f(x) = x² - 2x -4

And given that x = a = -1 and  x=b = 4

The average rate of change of the given function

$A(x) = \frac{f(b)-f(a)}{b-a}$

Step(ii):-

f(x) = x² - 2x -4

f(-1) = (-1)² - 2(-1) -4 = 1+2-4 = -1

f(4) = 4² -2(4) -4 = 16 -12 = 4

The average rate of change of the given function

$A(x) = \frac{f(b)-f(a)}{b-a}$

$A(x) = \frac{4-(-1)}{4-(-1)} = \frac{5}{5} = 1$

final answer:-

The average rate of change of the given function

A(x) =  1

Answer 2

Answer:

A(x) = 1

Step-by-step explanation:

$f(-1) = (-1)^{2} -2(-1)-4 == -1\\f(4) = (4)^{2} -2(4)-4 == 4$

When we plug this into the formula for rate of change we end up with...

$\frac{f(4)-f(-1)}{4-(-1)} \\= \frac{4-(-1)}{4+1} \\= \frac{5}{5}\\= 1$