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Chapter 2: Problem 73

Begin by graphing the square root function, \(f(x)=\sqrt{x} .\) Then use transformations of this graph to graph the given function. $$h(x)=\sqrt{-x+2}$$

Short Answer

Expert verified
The graph of the function \(h(x) = \sqrt{-x+2}\) is the graph of the square root function \(f(x) = \sqrt{x}\) reflected on the y-axis and shifted 2 units to the right.

Step by step solution

01

Graph the Base Function

Draw the graph of the function \(f(x) = \sqrt{x}\). This function represents a half-parabola, starting from point (0, 0) and rising to the right.
02

Understand the Transformation

The given function is \(h(x) = \sqrt{-x+2}\). Here, two transformations are taking place. The negative sign before \(x\) inside the square root indicates a reflection on the vertical line, while '+2' inside the square root indicates a horizontal shift to the right by 2 units.
03

Apply the Transformation

First reflect the original graph of the function \(f(x) = \sqrt{x}\) about the y-axis because of the negative sign. Then, shift the reflected graph to the right by 2 units due to '+2' inside the square root. This is your graph of function \(h(x) = \sqrt{-x+2}\).
04

Check Your Solution

Make sure that the new graph is a reflection of the original square root function and that it has been correctly shifted 2 units to the right.

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Most popular questions from this chapter

determine whether each statement makes sense or does not make sense, and explain your reasoning. My graph of \((x-2)^{2}+(y+1)^{2}=16\) is my graph of \(x^{2}+y^{2}=16\) translated two units right and one unit down.

will help you prepare for the material covered in the next section. $$ \text { If }\left(x_{1}, y_{1}\right)=(-3,1) \text { and }\left(x_{2}, y_{2}\right)=(-2,4), \text { find } \frac{y_{2}-y_{1}}{x_{2}-x_{1}} $$

How do you determine if an equation in \(x\) and \(y\) defines \(y\) as a function of \(x ?\)

Define a piecewise function on the intervals \((-\infty, 2],(2,5)\) and \([5, \infty)\) that does not "jump" at 2 or 5 such that one piece is a constant function, another piece is an increasing function, and the third piece is a decreasing function.

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