If you graph the function y = 3x and y = 3 –x the graphs create a reflection...

If you graph the function y = 3^x and y = 3 ^–x the graphs create a reflection about the y-axis. Explain why this occurs.

Now, if you graph the function y = 3^x and y = -(3^x) 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 = 3^x what would cause a reflection about the origin? Explain why this happens.

Expert Solution

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

milcah answered 1 year ago

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