Question

12.) For the multivariable function g(x,y)-x +y-2. create trace graphs for several appropriate values of each of x, y, and z. [12pts] -4 -1 -4 -2-

Answer 1

Let, z = x^{​​​​​​2}​​​​​+ y - 2

Now, for 1st graph.

Co-ordinates are x any y only.

So, z = 0

Now, we have to find two points (x1 , y1 ) and (x2 , y2 ) such that x^{​​​​​​2} + y - 2 = 0

i.e. x^{​​​​​​2} + y = 2 i.e. y = 2 - x^{​​​​​​2}

Let x = 1 so y = 1 so first point is (1,1)

Now, let x = 2 so y = 2 - (4) = ( 1 , -2 )

Hence second point is ( 1,-2)

Now draw a graph which passes through above 2 points.

Now, for second graph,

Graph containing 2 co-ordinates which are Y and Z

So, here X = 0

Thus, Z = (0) +y - 2. i.e. z = y - 2

Now, we will find 2 points (y1 , z1 ) and (y2 , z2)

Let, z = 1 so y will be z + 2 i.e. 1+2 = 3

So, (3,1) is first point

Now, let y = 1 so z will be -1

Thus, ( 1, -1 ) is second point

Now, draw a line which passes through above two points

Similarly, for third graph

Co-ordinate axes are X and Z

So, here Y= 0

Thus, Z = x^{​​​​​​2} - 2

Now, we will find two points (x1 , z1) and (x2 , z2 ) which satisfies equ z = x^{​​​​​​2} - 2

Let, x = 1 so z = 1 - 2 = -1

Let, x = 2 so, z = 4 -2 = 2

So, two points are (1 , -1 ) and ( 2 , 2)

Draw a line which passes through these points.

Hence the reqd.ans