SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. f(x) = 7 - x^4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM: Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither. f(x) = 7 - x^4      Log On


   

Question 161419: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
Determine whether the graph of the polynomial has y-axis symmetry, origin symmetry, or neither.
f(x) = 7 - x^4
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
if it has y axis symmetry then the values should be equidistant from the y-axis.
if it has x-axis symmetry then the values should be equidistant from the x-axis.
if it has origin symmetry then the values should be equidistant from the origin.
graph of the equation looks like:
scan below for further comments.
graph%28800%2C800%2C-10%2C10%2C-1000%2C1000%2C7-x%5E4%29
just looking at the graph i would say it would be symmetric to the y-axis only.
plotting some points may help as well.
equation is y = 7 - x^4.
x = 0, y = 7
x = +/- 1, y = 6
x = +/- 2, y = -9
x = +/- 3, y = -74
for every value of y, x is the same distance from the y axis.
my bet is symmetric to the y-axis.
a test is if you replace x with -x and the y value is the same, then the equation is symmetric about the x axis.
that is the case with this one.
good online explanation is at the following url.
http://tutorial.math.lamar.edu/classes/alg/symmetry.aspx