I need to sketch a function that is increasing and is concave up on [0,1]

I know the following:

- concave up refers to the second derivative where a<x<b
- Increasing refers to F(x2) > f(x1)

So how do I use the interval info to sketch the graph ? If , 0 is the x- axis & 1 is the y-axis am I making sure that the graph intersects at [0,1] above the x-axis and is heading upwards in order to fulfill the requirements of the question?

If so, where should the tail start ? Can I start it from say ... [-2,0] heading upwards & intersecting at the given interval [0,1] ?

It seems too arbitrary...