Answer to Question #264425 in Algebra for Paul Carpenter

Question

1. Find the domain of the function using interval notation.

f(x)= \frac{ \sqrt{x-6} }{ \sqrt{x-4}

2. Sketch a graph of a piecewise function. Write the domain in interval notation.

[Suggestion: for example, go to www.desmos.com/calculator and write

y=x^2 for {-1 ≤ x ≤ 1}

and

y = 3x - 2 {1 ≤ x ≤ 3}

Then choose your own functions and have fun.]

A sample graph using the example functions

3.

The cost in dollars of making x items is given by the function C(x) = 10x + 500.

a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item.

b. What is the cost of making 25 items?

c. Suppose the maximum cost allowed is $1500. What are the domain and range of the cost function, C(x)?