symmetry and graphs

[marshall1432]

1. Determine whether the graph of y = x3 is symmetric with respect to the x-axis, the y-axis, both axes or neither axis.

2. Determine whether the graph of y = x2 is symmetric with respect to the x-axis, the y-axis, both axes or neither axis.

3. If a graph is symmetric with respect to the x-axis and the point (7, -6) is on the graph, then what other point is also on the graph?

i dont know much about symmetry but i think:

1. respect to x-axis
2. respect to y-axis
3. (7,6)

i plugged them all in but didn't get a definite answer. if i know the answers i can backtrack to the problem and see what i did wrong. thats how i usually do it. can anyone help? thanks

 

[stapel]

well i plugged them all in but didn't get a definite answer.

It is unfortunate that you have not shown any work or reasoning. Since we have no idea what you might have done or what you might have thought about it, there seems little way of providing you help with whatever it was that you did. Sorry.

To determine symmetry, either look at the graph (and hope it's accurate), or else do the test:

. . . . .For a function f(x),
. . . . .if f(-x) = f(x), then the function is even, and
. . . . .if f(-x) = -f(x), then the function is odd.
. . . . .Otherwise, the function is neither.

In other words, plug -x in for x and simplify. If you get the same thing you'd started with (as would happen with, say, x⁴ - 3x² + 5), then the function is even. If you get the same thing but with every sign switched, "plus" for "minus" and vice versa (as would happen with, say, x³ + 4x), then the function is odd. If the result is anything else, then the function is neither.

Even functions are symmetric with respect to the y-axis.

Odd functions are symmetric with respect to the origin.

Functions cannot be symmetric with respect to the x-axis, but graphs of non-functions, such as ellipses, can be.

Eliz.