Question

The total cost of a vacation to a rain forest includes a fee of $560 for the tour guide, plus $630 per person. The function y=560+630x/ x

models the average cost per person, in dollars, when x people go on the vacation.

What is the horizontal asymptote of the function?


y= ????

Answer 1

Answer: y= 630 is the horizontal asymptote for the given function.

Step-by-step explanation:

Horizontal asymptotes are horizontal lines that the graph of the function approaches as x tends to $+\infty$ or $-\infty$.

Thus, If there is a function f(x),

Then Its horizontal asymptote,  y = $\lim_{x\rightarrow \infty} f(x)$

Here the given function is, $f(x) = \frac{560+630x}{x}$

Thus its horizontal asysmptote is, y = $\lim_{x\rightarrow \infty} \frac{560+630x}{x}$

⇒ y = $\lim_{x\rightarrow \infty}560/x+630$

⇒ y = 0+ 630

⇒ y= 630 is the horizontal asymptote of the given function f(x).

Answer 2

The horizontal asymptote of y = (630x + 560)/x is y = 630.

Linear function

A linear function is given by:

y = mx + b

where y, x are variables, m is the rate of change and b is the y intercept.

Given the total cost as y = 630x + 560.

For the function y = (630x + 560)/x, the horizontal asymptote is at:

y = 630x/ x = 630

The horizontal asymptote of y = (630x + 560)/x is y = 630.

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