Question

Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function?

Answer 1

Answer:

Step-by-step explanation:

Equation

f(x) = (8x + 1) / (2x + 9)

Notice the brackets. They are necessary to show what comes before the division sign, and what comes after.

Behavior

The best way to state the behavior is to get something like a graphing program to show you what the curve looks like -- where it's critical points are for example. I use Desmos for  this kind of question, Just do a search for Desmos and bookmark it. You will use it quite often.

So you want to know the behavior.

Right Curve

Crosses the x axis at (-0.125, 0)

Crosses the y axis at (0,0,111)

The right curve has a domain of -∞ < x < ∞

The  right curve has a range of -∞ < x < ∞

The range is going to have to go out quite a ways before you see any dramatic decrease in the way it is drawn.

Left Curve.

The right hand curve never crosses either the x or y axis.  Nor does it just touch the x or y axis.

The domain is -∞ <x < 0

The range is 0<x<∞