Maths-

General

Easy

Question

# A Software CD can be manufactured for each. The development cost to produce the software is . The first 200 CDs were used by testers to test the functionality of the software and were not sold.

a .Write a function f for the average cost , in dollars , of a sellable software CD , where x is the number of sellable software CDs

b. What are the vertical asymptotes of the graph ?

c. Graph the function

Hint:

### A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0.

Rational functions are of the form y=f(x)y=fx , where f(x)fx is a rational expression .

- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

## The correct answer is: The vertical asymptote of the rational function is x=0 .We will find more points on the function and graph the function.

### We have given that A Software CD can be manufactured for $0.10 each. The development cost to produce the software is $500,000. The first 200 CDs were used by testers to test the functionality of the software and were not sold.

X is the number of sellable software

As the total cost = $500000

And each CD costs $0.10

So, the function will be.

F(x) = (500000/x)+0.1(x+200) = (500000 + 0.1x^{2} + 20x) / x

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x = 0

The vertical asymptote of the rational function is x=0 .We will find more points on the function and graph the function.

x

y

600

913.333

2000

470

100

5030

X

Y

-800

-685

-4000

-505

-100

-4990

From the graph we can analyze that the vertical asymptote of the rational function is x= 0 and degree of the numerator is greater than the denominator, then there is no horizontal asymptote

So, the function will be.

F(x) = (500000/x)+0.1(x+200) = (500000 + 0.1x

^{2}+ 20x) / x

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x = 0

The vertical asymptote of the rational function is x=0 .We will find more points on the function and graph the function.

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