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Chapter 1: Problem 33

Use the algebraic tests to check for symmetry with respect to both axes and the origin. $$x^{2}-y=0$$

Short Answer

Expert verified
The graph of the equation \(x^{2}-y=0\) is symmetrical with respect to the y-axis, but it is not symmetrical with respect to the x-axis or the origin.

Step by step solution

01

Check for y-Axis Symmetry

Replace \(x\) with \(-x\) in the equation \(x^{2}-y=0\). The new equation becomes \((-x)^{2}-y=0\), which simplifies to \(x^{2}-y=0\). This is the same as the original equation, so the graph is symmetrical with respect to the y-axis.
02

Check for x-Axis Symmetry

Replace \(y\) with \(-y\) in the equation \(x^{2}-y=0\). The new equation becomes \(x^{2}-(-y)=0\), which simplifies to \(x^{2}+y=0\). This is not the same as the original equation, so the graph is not symmetrical with respect to the x-axis.
03

Check for Origin Symmetry

Replace \(x\) with \(-x\) and \(y\) with \(-y\) in the equation \(x^{2}-y=0\). The new equation becomes \((-x)^{2}-(-y)=0\), which simplifies to \(x^{2}+y=0\). This is not the same as the original equation, so the graph is not symmetrical with respect to the origin.

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Most popular questions from this chapter

Data Analysis: Light Intensity A light probe is located \(x\) centimeters from a light source, and the intensity \(y\) (in microwatts per square centimeter) of the light is measured. The results are shown as ordered pairs \((x, y)\) (Spreadsheet at LarsonPrecalculus,com) $$\begin{array}{lll} (30,0.1881) & (34,0.1543) & (38,0.1172) \\ (42,0.0998) & (46,0.0775) & (50,0.0645) \end{array}$$ A model for the data is \(y=262.76 / x^{2.12}\) A. Use a graphing utility to plot the data points and the model in the same viewing window. B. Use the model to approximate the light intensity 25 centimeters from the light source.

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