Interpret each piece of information,so that you can be able to sketch the graph of a function that satisfies the following conditions:

.(a)

.(b) , .

.(c)

.(c)

.(d)

.(d)

.

My interpretations are as follows:

.(a) y-intersect at (0,0)

.(b) Concave up for all values of , except at (possibly an asymptote there?)

.(c) As you approach 0 from the left, the slope approaches infinity and so the function gets higher.

.(c) As you approach 0 from the right, the slope approaches negative infinity and so the function gets lower.

.(d) As you approach negative infinity (left), the function gets lower and lower,

.(d) As you approach positive infinity (right), the function gets higher and higher.

I'm not to sure about them though, and it seems like (b) and (c) are contradictory (if C is true, that would mean concave down to the right of 0).

Did I mis-interpret these conditions or is there a flaw in the question?

UPDATE- Correct Answer is as follows: (thanks to Soroban)(changes in red)

.(a) y-intersect at (0,0)

.(b) Concave up for all values of x, except at x = 0 [ which is where g''(x) = 0 ].

.(c) As you approach 0 from the left, the slope is positive and it is getting more and more vertical (approaching infinity), and so the function is getting higher.

.(c) As you approach 0 from the right,and it is getting more and more vertical (approaching infinity), and sothe slope is negative.the function is getting higher

.(d) As you approach negative infinity (left), the function gets lower and lower,

.(d) As you approach positive infinity (right), the function gets higher and higher.

Therefore, the function is indeed concave up from the right side of 0.