Question

50 POINTS!

Determine which function has the greater rate of change, if either.


A. Function B has a greater rate of change because it's rate of change is 4/3

B. Function A has a greater rate of change because it's rate of change is 4/3

C. Neither function has a greater rate of change because their slopes are both 4/3

EXPLAIN

Answer 1

the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

so let's get two points from each table to get their slope or rate

for function A hmmm (2 , -5) and (6 , -2), and for function B hmmm (-5, -46) and (7 , -30)

`(\stackrel{x_1}{2}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{2}}}\implies \cfrac{-2+5}{4}\implies \stackrel{\textit{\Large A}}{\cfrac{3}{4}} \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-46})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-30})`

`\stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-30}-\stackrel{y1}{(-46)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{(-5)}}}\implies \cfrac{-30+46}{7+5}\implies \cfrac{16}{12}\implies \stackrel{\textit{\Large B}}{\cfrac{4}{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{\Large B}}{\cfrac{4}{3}}~~ > ~~\stackrel{\textit{\Large A}}{\cfrac{3}{4}}~\hfill`