ConjectureConsider the function f ( x , y ) = x 2 + y 2 . (a) Sketch the graph of the surface given by f . (b) Make a conjecture about the relationship between the graphs of f and g ( x , y ) = f ( x , y ) + 2 . Explain your reasoning. (c) Make a conjecture about the relationship between the graphs of f and g ( x , y ) = f ( x , y − 2 ) . Explain your reasoning. (d) On the surface in part (a), sketch the graphs of z = f ( 1 , y ) and z = f ( x , 1 ) .
ConjectureConsider the function f ( x , y ) = x 2 + y 2 . (a) Sketch the graph of the surface given by f . (b) Make a conjecture about the relationship between the graphs of f and g ( x , y ) = f ( x , y ) + 2 . Explain your reasoning. (c) Make a conjecture about the relationship between the graphs of f and g ( x , y ) = f ( x , y − 2 ) . Explain your reasoning. (d) On the surface in part (a), sketch the graphs of z = f ( 1 , y ) and z = f ( x , 1 ) .
Solution Summary: The author explains how to graph the surface of the function defined by f(x,y)=x2+y2.
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