Whats the symmetry of ?

Question

Hey guys, thank you in advance for your help, I am trying to see how I get this done. This is what I have to find out, any help on how to do it would be appreciate it. Thank you!

 

(a) Symmetric with respect to the y-axis
y = 3x3 − 3x
y = (x + 3)2
y = 3x − 3
y = 3x
y = 3x2 + 3
y = x + 3
none of the above

 

(b) Symmetric with respect to the x-axis
y = 3x3 − 3x
y = (x + 3)2
y = 3x − 3
y = 3x
y = 3x2 + 3
y = x + 3
none of the above

(c)    (−2, 1) is a point on the graph.
y = 3x3 − 3x
y = (x + 3)2
y = 3x − 3
y = 3x
y = 3x2 + 3
y = x + 3
none of the above

(e) Symmetric with respect to the origin
y = 3x3 − 3x
y = (x + 3)2
y = 3x − 3
y = 3x
y = 3x2 + 3
y = x + 3
none of the above

 

(f) Graph passes through the origin
y = 3x3 − 3x
y = (x + 3)2
y = 3x − 3
y = 3x
y = 3x2 + 3
y = x + 3
none of the above

Answer 1

Hi Franklin,

 

When talking about symmetry of a graph you need to understand the following points:

 

1. Symmetry with respect to the x-axis => for every point (x,y) on the graph there is also a point (x,-y) on the graph
2. Symmetry with respect to the y-axis => for every point (x,y) on the graph there is also a point (-x,y) on the graph
3. Symmetry with respect to the origin => for every point (x,y) on the graph there is a also a point     (-x,-y) on the  graph.

 

Therefore looking at question (a) - symmetry with respect to the y-axis, we will use the information in number 2 above. The way to test this in all the equations is to replace the x in each equation with -x and see that your equation still does not change.

Example:

Lets take the first equation in the question y = 3x³ − 3x. To see if the equation is symmetric with respect to the y-axis, replace each x with -x. => 3(-x)³ - 3(-x) = -3x³ + 3.

As you can see the equation has changed and is no longer the same, therefore we can say that this equation is not symmetric with respect to the y-axis. 

However the fifth equation y = 3x² + 3 when you replace the x by -x => 3(-x)² + 3 = 3x² + 3 the equation still stays the same. So this equation is symmetric with respect to the y-axis. 

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For question F a graph that passes through the origin has the point (0,0). Therefore any equation that y = 0 when x = 0, when graphed will pass through the origin.

 

I hope this helps!

Answer 2

OK WHAT I WOULD RECOMMEND IS TO GRAPH EACH ANSWER CHOICE INDIVIDUALLY, IF YOU DONT HAVE A GRAPHING CALCULATOR HANDY YOU CAN USE http://www.mathsisfun.com/data/grapher-equation.html.

 

 

AND THEN FOR EACH GRAPH SEE IF IT WILL SATISFY YOUR CRITERIA FOR A B C D E AND F.

 

FOR C IT MIGHT BE EASIEST TO JUST PLUG IN THE POINT INTO EACH EQUATION TO SEE IF IT WORKS.

 

FOR E, THE GRAPH WILL BE SYMMETRIC ABOUT THE ORIGIN IF THE GRAPH IS THE SAME WHEN YOU REFLECT ACROSS THE X AXIS AND THEN AGAIN OVER THE Y AXIS, OR SPIN IT 180 DEGREES.  THIS VIDEO MAY HELP... https://www.youtube.com/watch?v=EidP-Qh8blU

 

 

LET ME KNOW IF YOURE STILL TRIPPED UP