Which of the following functions has the same horizontal asymptote as the function graphed below?

Mathematics

1 answer:

Alla [95]3 years ago

7 0

Answer:

In most cases, there are two types of functions that have horizontal asymptotes. Functions in quotient form whose denominators are bigger than numerators when x is large positive or large negative.

Step-by-step explanation:

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The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013 (Source: U.S. Census Bureau). Find the

AleksandrR [38]

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.

to get the slope of any straight line, we simply need two points off of it, so let's use the ones provided in that

$\begin{array}{|cc|ll} \cline{1-2} \stackrel{years}{x}&\stackrel{population}{y}\\ \cline{1-2} 1990&1027974\\ 2013&688701\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{1990}~,~\stackrel{y_1}{1027974})\qquad (\stackrel{x_2}{2013}~,~\stackrel{y_2}{688701}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{688701}-\stackrel{y1}{1027974}}}{\underset{run} {\underset{x_2}{2013}-\underset{x_1}{1990}}} \implies \cfrac{-339273}{23}\implies -14751\qquad \stackrel{rate~of}{change}$