Question

For a fundraising project, your mathclub is publishing a fractal art calendar.The cost of the digital images and thepermission to use them is $850. Inaddition to these "one-time" charges,the unit cost of printing each calendaris $3.25.As x gets larger and larger, what does the end behavior of the function tell you about the situation?

Answer 1

In the given question, we are asked to explain what the end behavior of the given function tells you about the situation as x gets larger and larger.

Explanation

The function is given as;

$A=\frac{850+3.25x}{x}$

The end behavior is gotten as x tends to infinity

Therefore,

$\begin{gathered} \lim _{x\to\infty}A=\lim _{x\to\infty}\mleft(\frac{850+3.25x}{x}\mright) \\ =\lim _{x\to\infty}\mleft(\frac{850+3.25x}{x}\mright) \\ =\lim _{x\to\infty}\mleft(\frac{850}{x}+3.25\mright) \\ =\lim _{x\to\infty}\mleft(\frac{850}{x}\mright)+\lim _{x\to\infty}\mleft(3.25\mright) \\ =0+3.25 \\ =3.25 \end{gathered}$

Answer:

Therefore as x gets larger and larger, the function tends towards 3.25