This weekend I am going to teach you all how to check to see if a graph is symmetrical about the x axis, y axis, the line y = x, and the origin. These problems are fairly simple but there are some things that you need to know before you begin.
Notes:
About the x-axis
• First you put a negative in front of the y and simplify
• The new equation is symmetrical about the x-axis
• If the simplified equation matches the original equation then it is symmetrical about the x-axis
About the y-axis
• First you have to plug in a (-x)
• The new equation is symmetrical about the y-axis
• If the simplified equation matches the original equation then it is symmetrical about the y-axis
About the origin
• You have to plug in a (-x) and put a negative in front of the y
• The new equation is symmetrical about the origin
• If the simplified equation matches the original equation then it is symmetrical about the origin
About y = x
• You must switch the x and y and solve for y
• The new equation is symmetrical about y = x
• If the simplified equation matches the original equation then it is symmetrical about y = x
Example: xy^2 = 4x – 6
i. x(-y^2)=4x-6 no
ii. (-x)y^2=4(-x)-6 -xy^2=4(-x)-6 no
iii. (-x)(-y^2)=4(-x)-6 xy^2=4(-x)-6 no
iv. yx^2=4y-6 no
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