Graphing Rational Function...2

[nycmathguy]

Section 2.6
Question 24

Part (a)

Let R = all real numbers.

Domain = R except for t = 0.

Part (b)

Our t-intercept is the line t = 1/2.
When t = 0, f(t) is undefined. So,
no f(t)-intercepts.

Part (c)

Vertical Asymptote: t = 0.

Top degree = bottom degree.
So, our horizontal asymptote is -2/1 or simply -2.

Part (d)

Sketch by hand:

Desmos graph to confirm my sketch by hand.

 

[MathLover1]

correct

 

[nycmathguy]

correct

Wish I had more time to graph by hand. It's fun to draw graphs on the xy-plane.