Create a rational function, g(x) that has the following properties.

[CalcStruggler]

Create a rational function, g(x) that has the following properties:

 

[stapel]

Create a rational function, g(x) that has the following properties:

i) V.A.: None

ii) O.B.: None

iii) H.A.: y = 1

iv) Hole: [imath]\left(-4,\; -\frac{3}{19}\right)[/imath]

v) local min.: [imath]\left(-3,\; -\frac{1}{6}\right)[/imath]

vi) local max.: [imath]\left(1,\; \frac{1}{2}\right)[/imath]

I will guess that "V.A." stands for "vertical asymptote", "H.A." stands for "horizontal asymptote", "min." stands for "minimum", and "max." stands for "maximum". I'm pretty sure I know what is meant by "Hole". However, I cannot guess what "O.B." might mean.

When you reply with clarification, please include a clear listing of the information requested in the "Read Before Posting" message, starting with what you know about the rational function based on its having no vertical asymptote.

Thank you!

 

[Steven G]

Did you draw something that lives up to everything? I also would like to know what O.B. means. I bet it should have been O.A. for oblique asymptote

 

[Dr.Peterson]

Did you draw something that lives up to everything? I also would like to know what O.B. means. I bet it should have been O.A. for oblique asymptote

I agree; and I don't think this is possible. The HA, at least, has to be wrong; there may also be a missing x-intercept, if the actual HA is not y=0. (Or maybe they just aren't listing all the intercepts, local minima, etc.)

​

It isn't a very good problem. Where does it come from?