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Chapter 1: Problem 21

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=4-2 \sqrt{x}$$

Short Answer

Expert verified
The graph of the function \(f(x) = 4 - 2 \sqrt{x}\) is a transformed version of the standard square root function, with a vertical stretch by a factor of 2, a reflection across the x-axis, and a vertical shift upwards by 4 units. The graph decreases as x increases and lies within the viewing window of 0 鈮� x 鈮� 10 and -2 鈮� f(x) 鈮� 6.

Step by step solution

01

Identify Transformations

First, identify the transformations applied to the standard square root function to get the given function \(f(x) = 4 - 2 \sqrt{x}\). Notice that the whole function is multiplied by -2 and then 4 is added. This implies a vertical stretch by a factor of 2, reflection across the x-axis, and a vertical shift upwards by 4 units.
02

Set the Viewing Window

Next, set an appropriate viewing window. Since no specific domain or range was given, a standard viewing window would include positive real numbers for x, as the square root function is undefined for negative numbers, and real numbers for f(x). A reasonable window might be 0 鈮� x 鈮� 10 and -2 鈮� f(x) 鈮� 6.
03

Graph the Function using a Graphing Utility

After setting the viewing window, input the function \(f(x) = 4 - 2 \sqrt{x}\) into a graphing utility and generate the graph. The result should be a curve originating at (0,4), decreasing as x increases due to the reflection across the x-axis, with a vertical stretch due to the factor of -2, and shifted 4 units up.

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