A carpet installer charges a flat rate of $40, plus $1.50 per square foot for labor. So, the total cost for labor depends on the amount of carpet installed. The relationship between the total cost for labor and the amount of carpet installed is . The domain of the relation is x ≥ . The range of the relation is y ≥ .

We want to get the equation for the total cost and its domain and range.

The equation is:

c(x) = $40 + $1.50*x

domain: x > 0ft^2

range: y > $40.

First, let's get the equation.

We know that the carpet installer charges a flat rate of $40 plus $1.50 per square feet.

So if he/she works for x square feets, the cost is:

c(x) = $40 + $1.50*x

This is the cost equation.

Now we want to find the domain and range of this. The domain is given by the possible values of x that we can input in the function. Here we know that x must represent the number of square feet that are worked on, so it only must be a number larger than zero.

x > 0ft^2.

While the range is the set of the possible outputs.

The smallest possible output is the one we get when we evaluate the function in the smallest value of the domain, so we get:

y > $40.

These two define the domain and range.

If you want to learn more, you can read:

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 Domain

y = 40+1.5x  relationship

 range

Step-by-step explanation:

The domain is the amount of carpet installed.  We can install zero carpeting or any positive amount of carpeting.

Now writing the equation for the cost

They charge 40 flat rate plus 1.50 per square foot

y = 40+1.5x

Let x = 0

y = 40+0

Even if they do not install anything, they still charge 40 dollars flat rate.  That is the minimum amount we have to pay.  As x increases, the cost will increase.

That is the range, or the values of y

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