SOLUTION: Determine whether the graph of y= 3+ x^2 is symmetric with respect to the x- axis, the y-axis or the origin.

Question 785270: Determine whether the graph of y= 3+ x^2 is symmetric with respect to the x- axis, the y-axis or the origin.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
In the graph of all the points are above the x-axis , so it could not be symmetric with respect to the x- axis, or the origin.
Since , for each point (x,y) in the graph there is a corresponding (-x,y) point at the same distance to the other side of the y-axis, so it is symmetric with respect to the y-axis.
To be symmetric with respect to the y- axis, changing to should yield an equivalent equation, and that is true for .

To be symmetric with respect to the x- axis, changing to should yield an equivalent equation.
In this case, if is true, is definitely not true.

To be symmetric with respect to the origin, replacing for AND for AT THE SAME TIME should yield an equivalent equation.
In this case, if is true, <--> is definitely not true.
RELATED QUESTIONS
Determine whether the graph of y=x^3+1 is symmetric with respect to the origin the... (answered by Theo)

Determine whether the graph of y = |x| − 3 is symmetric with respect to the origin, (answered by math_helper)

Determine whether the graph of y = x3 +1 is symmetric with respect to the origin, the... (answered by robertb)

Determine whether the graph of the equation is symmetric with respect to the x-axis,the... (answered by Fombitz)

Determine whether the graph of y = | x | + 3 is symmetric with respect to the origin, the (answered by ccs2011)

Please help determine whether the graph of y = x^2 + 9 is symmetric with respect to the... (answered by stanbon)

Determine whether x^2+y-81=0 is symmetric with respect to the x-axis, y-axis and or... (answered by math-vortex,robertb)

Determine whether the graph of y=4x^2+1 is symmetric with respect to the x-axis, y-axis,... (answered by MathLover1)

determine the symmetries (if any) of the graph of the given relation 5y^3=6x^3+2 is... (answered by MathLover1)