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DochEvi [55]
2 years ago
12

Given the function f(x) = 3x - 1, explain how to find the average rate of change between x = 1 and x = 4.

Mathematics
2 answers:
Mice21 [21]2 years ago
6 0

Step-by-step explanation:

f(1) = 3×1 - 1 = 2

f(4) = 3×4 - 1 = 12-1 = 11

so, the functional value changes 11-2=9 units on an x interval of 4-1=3 units length.

the average change rate is the total change across the x interval relative to the interval length.

that is

9/3 = 3

which is the slope (= the factor of x) in the line equation.

for a line its change rate for any point is the same constant. and that is therefore automatically also the average change rate across an interval of x values.

if the change rate would be different for different parts of the function, it would not be a straight line.

Tems11 [23]2 years ago
6 0

Answer:

3

Step-by-step explanation:

The average rate of f(x) in the closed interval [ a, b ] is

\frac{f(b)-f(a)}{b-a}

Here [ a, b ] = [ 1, 4 ] , then

f(b) = f(4) = 3(4) - 1 = 12 - 1 = 11

f(a) = f(1) = 3(1) - 1 = 3 - 1 = 2

average rate of change = \frac{11-2}{4-1} = \frac{9}{3} = 3

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