In the previous section, a general introduction of each representation was given to describe the function V = 8√h. In this section, you will continue to work with tables of square roots.

A carpet store uses the function, c(a) = 15.5√a + 26.5, to determine the cost, c, in dollars to install carpet, where a represents the area of the room to be carpeted.

How much would it cost if the rectangular room you wanted to carpet was 13 feet by 13 feet? What if you had a second room that was double the dimensions of the first room? Would the cost double as well? Knowing the characteristics of square root functions can help you analyze these questions.

First, create a table of values for this function. You may use your graphing calculator to obtain the values, or click the applet below.

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Need additional directions?

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a	Process	C
0	15.5√0 + 26.5	26.5
100	15.5√100 + 26.5	181.5
121	15.5√121 + 26.5	197
144	15.5√144 + 26.5	212.5
169	15.5√169 + 26.5	228
225	15.5√225 + 26.5	259
676	15.5√676 + 26.5	429.5

Conclusion Questions

• What is the cost to carpet a room with dimensions of 13 feet by 13 feet?

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  To find the area of the room, first multiply 13 × 13. You get 169 square feet. Looking at the table above, you see that it would cost $228 to install carpet in a room with an area of 169 square feet.

• How would doubling the dimensions of the room affect the cost?

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  Doubling the dimensions gives you dimensions of 26 feet × 26 feet, which results in an area of 676 feet squared. Looking at the table, the cost to lay carpet for a room that has an area of 676 feet squared is $429.50. Doubling the dimensions did not double the cost.

• Why are there no values less than zero in the table?

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  The values of a represent the area of the room. Since area cannot be less than zero, it would not make sense to include negative values. Similarly, you could not have a cost less than zero. Also, if you take the function out of the context of area and cost, taking the square root of a negative number gives you a non-real number.

Pause and Reflect

The function f(x) = √x + 1 − 5 is a transformation of the parent square root function. What is the transformation?

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The function has been translated to the left 1 unit and down 5 units.

How does this transformation help you predict the graph?

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The parent square root function begins at the origin and gradually rises up to the right. The transformation informs you that the graph begins at the point (−1, −5) and gradually rises up to the right like the parent function.

Practice

1. The parent square root function has been translated to the right 4 units. Create a table to represent this new function.

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   Start with the x-value that would make the number under the radical sign equal to zero.

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   The algebraic representation of the translated function is f(x) = √(x – 4).
   Here is a table of possible values.
   

   x	f(y)
   4	0
   5	1
   8	2
   13	3
   20	4

   

2. Explain why there would be no x-values less than −2 in a table that represents the square root function f(x) = √(x + 2) – 3?

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   Try substituting a number less than -2, and see what happens.

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   Check Your Answer

   x-values less than −2 would result in a negative number under the radical. Taking the square root of a negative number will give you a non-real number.

3. Complete the table for the equation y = 2√x + 2 + 10.
   
   

   x	Process	y
   -2	2√(-2) + 2 + 10
   -1		12
   	2√(2) + 2 + 10
   7		16
   14
   x		y

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   Fill in the top row first. Compare the x and y values to the process column to help you determine the remaining empty boxes.

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   x	Process	y
   -2	2√-2 + 2 + 10	10
   -1	2√-1 + 2 + 10	12
   2	2√2 + 2 + 10	14
   7	2√7 + 2 + 10	16
   14	2√14 + 2 + 10	18
   x	2√x + 2 + 10	y