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

Question

Describe how the graph of g is obtained from the graph of f.

(a)   g(x, y) = f(x, y) + 4

1) shift 4 units in the positive x direction

2) shift 4 units in the positive y direction

3) shift 4 units in the positive z direction

4) stretch vertically by a factor of 4

5) reflect about the xy-plane

(b)   g(x, y) = 4f(x, y)

1) shift 4 units in the positive x direction

2) shift 4 units in the positive y direction

3) shift 4 units in the positive z direction

4) stretch vertically by a factor of 4

5) reflect about the xy-plane

(c)   g(x, y) = f(x, y)

1) shift 1 unit in the negative x direction

2) shift 1 unit in the negative y direction

3) shift 1 unit in the negative z direction

4) reflect about the xz-plane

5) reflect about the xy-plane

(d)   g(x, y) = 4 f(x, y)

1) shift 4 units in the negative z direction

2) reflect about the xy-plane then shift 4 units in the positive z direction

3) shift 4 units in the negative z direction and shrink vertically by a factor of 4

4) shrink vertically by a factor of 4

5) shift 4 units in the positive z direction then reflect about the xy-plane

Describe how the graph of g is obtained from the graph of f g(x, y)-r, y) + 4 O shift 4 units in the positive x direction (a) Oshift 4 units in the positive y direction shift 4 units in the positive z direction Ostretch vertically by a factor of4 O reflect about the ay-plane g(x,y)-x, y) shift 4 units in the positive x direction shift 4 units in the positive y direction (b) O shift 4 units in the positive z direction O stretch vertically by a factor of4 O reflect about the xy-plane (c) olx, y)-x, Oshift 1 unit in the negative x direction Oshift 1 unit in the negative y direction shift 1 unit in the negative z direction O reflect about the xz-plane O reflect about the xy-plane (d) x, y)-4-Rx,y shift 4 units in the negative z direction O reflect about the xy-plane then shift 4 units in the positive z direction Oshift 4 units in the negativez direction and shrink vertically by a factor of 4 O shrink vertically by a factor of 4 shift 4 units in the positive z direction then reflect about the xy-plane

Explanation / Answer

(a)   g(x, y) = f(x, y) + 4

+ 4 shifting it in positive z direction

3) shift 4 units in the positive z direction ( answer)

b)   g(x, y) = 4f(x, y)

4) stretch vertically by a factor of 4(answer)

c)   g(x, y) = f(x, y)

(4)reflect about the xz-plane

(d) g(x, y) = 4 f(x, y)

(5) shift 4 units in the positive z direction then reflect about the xy-plane

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