Sketch and make an algebraic expression to model graph

[Jinxypo]

Homework Statement

Sketch the graph of a function g(x) with a corresponding domain on (-5, infinity) whose first derivative is always positive and whose second derivative is always negative. Then come up with and algebraic expression to model your graph.

Homework Equations

The Attempt at a Solution

I know that the first derivative is positive, therefore g(x) is always increasing. Also the second derivative is always negative, therefore g(x) is concave down. The graph I drew to model this looks like the following picture. Two points on my graph include, (-5,1) and (-1,5) with a horizontal asymptote at y = 6. http://i5.photobucket.com/albums/y165/RDH_TheOne/d4567def.jpg" I just don't know how to come up with the expression that models my graph any help will be appreciated.

 

[Mark44]

Homework Statement

Sketch the graph of a function g(x) with a corresponding domain on (-5, infinity) whose first derivative is always positive and whose second derivative is always negative. Then come up with and algebraic expression to model your graph.

Homework Equations

The Attempt at a Solution

I know that the first derivative is positive, therefore g(x) is always increasing. Also the second derivative is always negative, therefore g(x) is concave down. The graph I drew to model this looks like the following picture. Two points on my graph include, (-5,1) and (-1,5) with a horizontal asymptote at y = 6. http://i5.photobucket.com/albums/y165/RDH_TheOne/d4567def.jpg" I just don't know how to come up with the expression that models my graph any help will be appreciated.

Do you know about the transformations that cause the graph of a function to be shifted or reflected across an axis? A function that comes to mind is y = 1/x, for x > 0. If you shift it to the left and up, and reflect it across the x-axis, you get a function that meets the requirements of this problem.

 

[Jinxypo]

Thanks Mark,
I've come up with the following equation, could you please double check to see if it's right.
y = -(1 / x+5) for x > -5

 

[Mark44]

That works, but you should write it as y = -1/(x + 5), for x > -5. This graph is asymptotic to the x-axis, not the line y = 6 as you wanted. If you want it to be asymptotic to y = 6, shift it up by 6 units.

 

[Jinxypo]

Thank you very much Mark you've been a great help.