Test the equation for symmetry about the xaxis yaxis and the

Test the equation for symmetry about the x-axis, y-axis, and the origin.y=2^x + 2^-x.

Solution

Test for symmetry about the y-axis: Replace x with (-x). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the y-axis.

Test for symmetry about the x-axis: Replace y with (-y). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the y-axis.

the given original equation is y = 2^(x) + 2^(-x)

checking symmetry about x- axis :

replace y with -y in original equation

-y = 2^(x) +2^(-x)

but this is not equal to the original equation

so this not symmetric about x axis.

checking symmetry about y-axis:

replace x with -x

y= 2^(-x)+2^(-(-x))

y = 2^(-x) +2^(x)

rearrage the terms

y = 2^(x) +(2^-x)

this is equal to original equation

so this is symmetric about y-axis

checking symmetry about origin:

replace x with -x and replace y with -y

the equation becomes

-y = 2^(-x) +2^(-(x))

-y = 2^(-x) +2^(x)

-y =2^(x) +2^(-x)

so this not equal to the given equation

so this not symmetric about origin