Algebraic tests

Question

Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.)

x² − y = 9

x-axis symmetry

y-axis symmetry

origin symmetry

no symmetry

Answer 1

Algebraic tests

x-axis symmetry

when “y” is replaced with “-y”,  and the new equation is equivalent to the original equation

x² - (-y) = 9

x² + y = 9

not equivalent

y-axis symmetry

when “x” is replaced with “-x”,  and the new equation is equivalent to the original equation

(-x)² – y = 9

x² – y = 9

equivalent

origin symmetry

when “x” is replaced with “-x”,  and “y” is replaced with “-y”,  and the new equation is equivalent to the original equation

(-x)² -  (-y) = 9

x² + y = 9

not equivalent

Answer

y-axis symmetry

Answer 2

f(x)=y=x²-9

f(-x)=f(x)...what does this tell you about symmetry

Since f is a function, it CANNOT be symmetric about the x-axis....Why?

And what do the above 2 facts tell you about symmetry about the origin?