Determine whether the graph of each equation is symmetric with re...

Question

Determine whether the graph of each equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of those, or none of these. x^2 + y^2 =17

Accepted Answer

Hello. Today we're gonna be evaluating the symmetry of a graph without actually graphing the equation. So the equation given to us is why is equal to X to the one third power. Now I'm gonna go ahead and rewrite this by using our power rule for exponents. So the exponent power rule states that we have one third as our exponents. Then we can rewrite this as the cube root of X. So why is equal to the cube root of X? Now, what does this tell us? Well, this is the graph of a square root function in the form of Y is equal to the nth root of X. And the conditions of this graph is that if N is even you have symmetry about the y axis and if N is odd, you have symmetry about the origin in this case here, N is going to be three. And we know that three is an odd number since three is an odd number. That tells us that we're going to have symmetry about the origin. So now we know that the graph is going to have symmetry about the origin. That means that the solution to this problem is going to be C. So I hope this video helps you identify the symmetry of an equation and I'll go ahead and see you all in the next video

Watch next