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# Evaluating and graphing the given functions

1. Evaluate the function f(x) = 9x - 6 for x=0.

2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

3. Find the slope of the line through the points ( 5, -5) and ( 6, -1)

4. Kafka Inc. imports hard drives and sells them on the internet. The profit is given by the equation P = 140n - 8500, where n is the number of hard drives sold. Graph P = 140n - 8500 for n < 1000. Estimate the profit, to the nearest ten dollars, corresponding to the sale of 875 hard drives.

5. When \$ 8500 is invested in a savings account paying simple interest for the year, the interest, i in dollars, can be obtained from the equation i = 8500r , where r is the rate of interest in decimal form. Graph i = 8500r , for r up to and including a rate of 16%. If the rate is 12%, how much interest is earned?

#### Solution Preview

Please refer attached file for graphs and better clarity of expressions.

1. Evaluate the function f(x) = 9x - 6 for x=0.

f(x)=9x-6
f(0)=9*0-6=3

2. Bob owns a watch repair shop. He has found that the cost of operating his shop is given by C(x) = 4x2-296x+85 , where c is cost and x is the number of watches repaired. How many watches must he repair to have the lowest cost?

C(x)=4x^2-296x+85
Differentiate with respect to x, we get
C'(x)=8x-296
Put C'(x)=0
8x-296=0
x=296/8=37

Let us find second derivative of C(x)
C''(x)=8

We find that it ...

#### Solution Summary

There are five problems. Solutions to these problems explain the steps to evaluate and graph the given functions. Solutions also explain the methodology to find the slope of a line passing through the two given points.

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