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1 answer:
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Answer:
- 9
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [a, b ] = [ - 5, 2 ], thus
f(b) = f(2) = 2² - 6(2) + 2 = 4 - 12 + 2 = - 6
f(a) = f(- 5) = (- 5)² - 6(- 5) + 2 = 25 + 30 + 2 = 57 , thus
average rate of change = =
= - 9
Step 1
<u>Find the slope of the function f(x)</u>
we know that
The formula to calculate the slope between two points is equal to
Let
substitute
Step 2
<u>Find the y-intercept of the function f(x)</u>
The y-intercept is the value of the function when the value of x is equal to zero
in this problem the y-intercept of the function is the point
so
the y-intercept is equal to
Step 3
Verify each case
we know that
the equation of the line into slope-intercept form is equal to
where
m is the slope
b is the y-intercept
<u>case A) </u>
In this case we have
therefore
the function of case A) does not have the same slope as the function f(x)
<u>case B) </u>
In this case we have
therefore
the function of case B) does not have the same slope and y-intercept as the function f(x)
<u>case C) </u>
In this case we have
therefore
the function of case C) does have the same slope and y-intercept as the function f(x)
<u>case D) </u>
In this case we have
therefore
the function of case D) does not have the same y-intercept as the function f(x)
therefore
<u>the answer is</u>