In: Math
If you graph the function y = 3x and y = 3 –x the graphs create a reflection about the y-axis. Explain why this occurs.
Now, if you graph the function y = 3x and y = -(3x) the graphs create a reflection about the x-axis instead. Explain why, in detail, the reflection changes from being about the y-axis to being about the x-axis.
Now, know the answers to #11 and #12, if we take the base function y = 3x what would cause a reflection about the origin? Explain why this happens.
Looking at function
, we get some point on this graph as , for x = 0 we have y = 1 ,
and for x = 1 we have y = 3 , for x = -1 we have y = 1/3 so points
are ,
now for the function
, giving our previous x values we get , for x = 0 , y = 1 , for x
= 1 we get y = 1/3 and for x = -1 we get y = 3 , which
shows that y value gets interchanged between positive and negative
value of x , which means graph gets reflected about y axis
.
now for the function
, giving our previous x values we get , for x=0 , y = 1 , for x =
1 , y = -3 and for x = -1 , y = -1/3 which shows that the y
value gets negative value for our given x values , which
says that graph gets reflected about y axis ,
Since the graph
does not show any symmetry that is
, the graph cannot show a reflection about origin , in order to
have reflection about origin it should satisfy this