The average rates of change of f(x) and their corresponding intervals are given as:
Interval Rate of Change
[-5, -1] -8
[-4, -1] -7
[-3, 1] -4
[-2, 1] -3.
<h3>What is the explanation for the above?
</h3>
Step 1 - See Table Attached
Step 2 - State the formula for rate of change
The formula for rate of change is given as:
= [change in f(x)] / [change in x]
a) For interval [5, -1] ⇒
Rate of Change - [ f(1) - f(-5) ] / [-1 - (-5)]
= [-1 - 35] / [-1+5]
= -36 / 4
= - 8
b) For interval [-4, -1] ⇒
rate of change = [ f(-1) - f(-4) ] / [ -1 - (-4) ]
= [3 - 24] / [-1 + 4]
= -21/3
= - 7
c) interval [-3,1] ⇒
rate of change = [ f(1) - f(-3) ] / [ 1 - (-3) ]
= [-1 - 15] / [1 + 3]
= -16/4
= - 4
d) interval [-2,1] ⇒
rate of change = [f (1) - f(-2)] / [1 - (-2)]
= [ -1 - 8] / [1 + 2]
= -9/3
= -3
Learn more about rate of change at:
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Answer:
m - 7 = -13 + m
Step-by-step explanation:
Answer:
Suppose we have a polynomial of degree N with a leading coefficient A and roots {x₁, x₂, ..., xₙ}
We can write this polynomial as:
P(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)
such that the terms:
(x - x₁), (x - x₂), etc...
are called the factors.
In this case, we know that the roots OF THE FACTORS
are:
(x = - 2)
(x = - (1 + √5))
(x = + 3i)
If the root of the polynomial is x = -2, then the factor should be:
(x + 2)
which is zero when we evaluate x in -2
Then the correct option is the first one.
