Determine whether each equation has a graph that is symmetric wit...

Question

Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. 
y^3 = x + 4

Accepted Answer

Identified at the graph defined by the following equation is symmetric with respect to the origin X axis Y axis or nine where we have three Y to the fifth is equal to X minus seven. Now let's check the X axis symmetry first X axis to check the X axis symmetry. We're gonna say why is equal to negative Y. In other words, we're gonna place Y with negative Y. Now you want to see when we do this, do we get the same function back out? So let's see we have three times native Y to the 5th Equal to X -7. To simplify this negative Y to the fifth is just negative Y to the fifth To Native three Wise V is equal to X -7. Now, this is not equal to our original equation. So that is a note that is not smash fel on the X axis. Let's take the Y axis for the Y axis. We want to see if we replace X with negative X will we get the same number or same equation rather. So three Y -5 is equal to negative X -7. Well, we simplify Native X -7 Like. So that is also not equal to the original equation. So you'll say X or Y axis symmetry is also no good. Let's also check the origin for the origin. We want to replace both with native Y and native X CF three, negative Y to the fifth is equal to negative X minus seven where we get negative three Y to the fifth, It's equal to negative X -7. That is not equal to our original. So this is also not symmetrical around the origin. We can then say that the answer to our problem is answer D the graph does not have any symmetry. Okay. I hope to help you solve the problem. Thank you for watching. Goodbye.

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Determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. y^3 = x + 4