Question

Given the function f(x) = 2(3)x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Answer 1

f(0) = 2(3)(0) = 0  ⇒  (0, 0)

f(1) = 2(3)(1) = 6  ⇒  (1, 6)

rate of change from x = 0 to x = 1

$\frac{y2 - y1}{x2 - x1}$ = $\frac{6 - 0}{1 - 0}$ = $\frac{6}{1}$ = 6

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f(2) = 2(3)(2) = 12  ⇒  (2, 12)

f(3) = 2(3)(3) = 18  ⇒  (3, 18)

rate of change from x = 2 to x = 3

$\frac{y2 - y1}{x2 - x1}$ = $\frac{18 - 12}{3 - 2}$ = $\frac{6}{1}$ = 6

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Since it is the same line, they will have the same slope (aka rate of change).