Emma M.

asked • 02/05/17

Describe the graph

How could the graph of y=2x^3+1 be used to graph y=-2x^3+1?
 

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Mark M. answered • 02/06/17

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y = 2x3 + 1
 
Replace x by -x:  y = 2(-x)3+1 = -2x3+1
 
Replacing x by -x reflects the graph of y = 2x3+1 in the y-axis.  
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Michael J.

The negative sign only affects the x3 term.  Not the whole function.  When you flip it (vertically due to negative sign on that term), the y-intercept still remains the same.   It should be a reflection about the line   y=1.  If you graph, you will see.
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02/06/17

Mark M.

tutor
Yes.  The y-intercept stays the same because it's on the axis of reflection (the y-axis).  For any function y = f(x), replacing x by -x reflects the graph in the y-axis.  
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02/06/17

Mark M.

tutor
I meant the y-axis.  I have corrected my solution.  
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02/06/17

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