Describe how the graph of g is obtained from the graph of f. g(x, y) = f(x, y) +

Question

Describe how the graph of g is obtained from the graph of f. g(x, y) = f(x, y) + 8 shift 8 units in the positive x direction shift 8 units in the negative x direction shift 8 units in the positive y direction shift 8 units in the negative y direction shift 8 units in the positive z direction shift 8 units in the negative z direction stretch vertically by a factor of 8 shrink vertically by a factor of 8 reflect about the xy plane g(x, y) = 8f(x, y) shift 8 units in the positive x direction shift 8 units in the negative x direction shift 8 units in the positive y direction shift 8 units in the negative y direction shift 8 units in the positive z direction shift 8 units in the negative z direction stretch vertically by a factor of 8 shrink vertically by a factor of 8 reflect about the xy plane g(x, y) = -f(x, y) Shift 8 units in the positive x direction shift 8 units in the negative x direction shift 8 units in the positive y direction shift 8 units in the negative y direction shift 8 units in the positive z direction shift 8 units in the negative z direction stretch vertically by a factor of 8 shrink vertically by a factor of 8 reflect about the xy plane g(x, y) = 8 - f(x, y) shift 8 units in the positive x direction shift 8 units in the negative x direction Shift 8 units in the positive y direction shift 8 units in the negative y direction shift 8 units in the positive z direction then reflect about the xy plane shift 8 units in the negative z direction stretch vertically by a factor of 8 shrink vertically by a factor of 8 reflect about the xy plane then shift 8 units in the positive z direction

Explanation / Answer

Hello, Welcome to chegg.

So 1st we see some genral shifting and scaling and then we see about the Questions.

So if we have a graph of f(x,y)

then we do some modification and make graph g(x,y) from f(x,y)

So there are different type of Modifcations,

Some are shiftign in both direction, scaling

So.

-->> if g(x,y) = f(x,y)

Both are same.

-->>g(x)= f(x)+h

So if h is +ve then it means that the graph g(x) value is h more then f(x) value at that point.

or we can say that if h>0 then f(x) is shifted h upword direction. or in +ve y direction.

and if h<0 then the graoh f(x) is shifted h downword in the -ve y direction.

So same hapens in the 3D also.

In 3D both are shofted in the +ve Z or -ve Z directions.

-->> g(x,y) = kf(x,y)

So if k>1 then it straches the graph vertically and if 0<k<1 then it shrink the graph verticaly.

and if k = -1

then the graph is reflect about the xy plane.

So we see question one by one.

(a) g(x,y) = f(x,y)+8

SO the graph f(x,y) is shofted 8 unites in the +ve z direction.

(b) g(x,y) = 8 f(x,y)

The graph is stretched verticaly by a factor 8.

(c) g(x,y) = -f(x,y)

The graph is reflected by the Plane xy.

or we can say Plane z = 0 {xy plane }

(d) g(x,y) = 8-f(x,y)

So we get this by

--> 1st g(x,y) = -f(x,y)

Reflect about the xy Plane .

then

--> 2nd g(x,y) = -f(x,y)+8

Shift 8 units in the +ve z direction.

So these are the answers of the Questions

(a) ->>(5)

(b) ->>(7)

(c) ->>(9)

(d) ->>(9)

Thank You

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