4. Find fractional linear transformations f satisfying f(z) = w; for i = 1,2,3 if (a) z1=1, z=0, 23 = -1; w₁ = 0, w₂ = -i, w3 = 0. (b) ₁i, 220, 23 = -1: w₁ = -i, w2 = 0, w3 = ∞0. == w1

Define linear transformations S : P1 --->  P2 and T: P2---> P1 by                       S(a + bx) = a + (a + b )x + 2bx2 and T ( a + bx + cx2) = b + 2cx            Compute (S 0 T)(3 + 2x - x2) and (S 0 T)(a + bx + cx2).                                          Can you compute ( T 0 S) (a + bx) ? If so, compute it.

Which function represents a transformation that moves a figure to the right 3 units and down 7 units? (x, y) → (x - 3, y + 7) х, у) —> (х + 3, у +7) (х, у) —> (х + 3, у — 7) О (г, 9) — (2 — 3, у — 7)

Find the linearization L(x,y) of the function at each point. f(x у) — х2 + у2 +1 а. (1,1) b. (4,2) a. L(x,y) =| b. L(x,y) =|

find the derivative of (z+j)? j2:+2z z4+ j4z³+6z² – j4z+1 j2:2-2z 24+j4z–6z2 – j4z+1 j2:+2z 24+j4:-6z2+j4z+1 j2:2 -2z z4 - j4z+6z² – j4z+1

Determine a mapping of the form (x, y)) from y = f(x) for each of the following. y = 3f(2x) y=-11 7x y=-2r(-3x)

Q. What transformation is happening? (x, y) ----> (x + 2, y - 3) Slide up 2, left 3 Slide right 2, down 3 Slide right 2, up 3 Slide left 3, right 2

2 Suppose y is a function of x such that y and y(4) = -3. Find y.