How to Determine Symmetry About x-axis, y-axis or Origin?

Question

Determine of R(x) = (x^2 - 5x + 4)/(x^2 +7x +6) is symmetric about the x-axis, y-axis or origin.

Answer 1

A function cannot be symmetric about x-axis... For example the circle x^2 + y^2 = 25 with center (0,0)

and radius 5 it is not a function because if x = 0 there are tow images y = 5 and y = -5, but the graph is symmetric about x-axis.



For a function the rule is... if f(-x) = f(x) it is an even function and the graph is symmetric about y-axis



and if f(-x) = -f(x) it is an odd function and the graph is symmetric about origin.



Then for a function just change x by -x and verify if f(x) changed or not the signal.



Here R(x) is a function, then it is not symmetric about x-axis.



Here we use the rule, change x by -x and get R(-x) = (x^2 +5x +4)/(x^2 -7x + 6). Here R(-x) it is not the same as R(x) then it is not an even function, it is not symmetric about y-axis ....

Here R(-x) is not the same as -R(x), then it is not an odd function then it is not symmetric

about origin.



Then the function R(x) has no Symmetry about x-axis, y-axis and origin. OK!

Answer 2

good day, i'm no longer likely to attempt in the adventure that your equation 0=x^4+4x^3+sixteen is right. by way of fact if we glance at it on the style 0=(x-2)^2(x+2)^2 it rather is extra helpful straight forward to comprehend the respond. what fee of x on the fabulous ingredient will circulate back 0? 2 and -2! i wish that helped :]

Answer 3

for symmetry about y axis f(x)=f(y)

for symmetry about x axis f(-x)= - f(x)



simply substitute - x in place of x and find out