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Chapter 1: Problem 22

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$h(x)=\sqrt{x+2}+3$$

Short Answer

Expert verified
The graph of the function \(h(x)=\sqrt{x+2}+3\) starts at the point (-2, 3) and continues to the right, above the x-axis, within the set viewing window of \([-2,10]\) for x and \([0,10]\) for y.

Step by step solution

01

Identify the Function

Recognize the function \(h(x)=\sqrt{x+2}+3\). This is a transformed square root function where the function is shifted two units to the left and three units upward.
02

Identify the Domain and Range

The square root of a number is only defined for non-negative numbers. As we have \(x+2\) under the square root, this function will be defined for all 麓x麓 such that \(x+2 \geq 0\). This means that \(x \geq -2\). The range of this function will be all numbers greater than or equal to 3, as the minimum value of \(\sqrt{x+2}\) is 0, but this has been translated three units up.
03

Choose an Appropriate Viewing Window

Based on the chosen domain and range, pick an appropriate viewing window. For the x-values, you can start at -2 and go to some positive number. For the y-values, starting at 0 will take into account the whole range of function. Let麓s use the window \([-2,10]\) for x and \([0,10]\) for y.
04

Graph the Function

Input the function \(h(x)=\sqrt{x+2}+3\) into the graphing utility and set the viewing window as decided in the previous step. The graph will start at the point (-2, 3) as the square root of zero is zero, which when added to 3 gives 3.

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