Is 2,4 and 3,9 and 4,16 a linear function?

No, it is not a linear function.

Step-by-step explanation:

If you look at the change in the x-values, you'll see that it increases by 1 each time. But, if you look at the y-values, you'll see that they don't change by the same increment as it goes from 4 to 9 (which means it increased by 5) and from 9 to 16 (which means it increased by 7). For it to be considered a linear function, the change in the y-value has to be the same every time for each increment in the x-value.

If you're ever in doubt, just graph the points on a piece of paper and see if they form a straight line. If they do, then it is a linear function. If they don't then its not linear.

Hope this helps!

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.