Hi can you check if these answers are correct?

1. Sketch the graph of a function that satisfies these conditions:

limf(x) = 2

x->0-

lim f(x) = 0

x->0+

limf(x)=3

x->4-

limf(x)=0

x->4+

f(0) = 2

f(4) = 1

Does this give me the these points?

(0,2) approaching from the left

(0,0) approaching from the right

(4,3) approaching from the left

(4,0) approaching from the right

(0,2)

(4,1)

Also, since I have the point (0,2) twice, is there anything special I need to do with it?

2. Determine the infinite limit

lim (x^{2}+ 1) / (x^{2}- 4x + 4)

x->2-

= (x(x-2)) / (x-2)(x-2)

= x / (x-2)

=2 / 0 = positive infinity

3. Graph this function

y=(x^{2}+1) / (3x-2x^{2})

How do i graph this without using a calculator?