Determine the function which corresponds to the given graph.
the asymptote is x = -3.

y = log (x + 3)

Step-by-step explanation:

This function (graph) is a translated version of the log function.

The basic graph of y = log(x) is attached.

As we can compare, we see that the basic logx graph goes through (1,0) and the asymptote is x = 0

This graph, is basically translated 3 units left, so the point becomes (1-3,0) = (-2,0) and the asymptote becomes x = -3.

THis conforms with the graph shown.

Thus, we need to horizontally translate y = log x 3 units left, which means:

y = log (x + 3)

Note: if we have a horizontal translation of a units to the left, y = logx becomes y = log(x+a)

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.