F(x)=x; vertical stretch by factor o 2 followed by translation 1 unit up

think of this as a composition of functions.

let h(x)=x−2 be our horizontal translation and g(x)=−x be our reflection

(f∘g)(x)=f(−x) is our function reflected.

(f∘h)(x)=f(x−2) is our function translated.

(f∘g∘h)(x) is our function first translated then reflected.

(g∘h)(x)=−(x−2)=2−x(f∘g∘h)(x)=f(2−x)

(f∘h∘g)(x) is our function first reflected then translated.

(h∘g)(x)=g(x)−2=−x−2(f∘g∘h)(x)=f(−x−2)

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.