Question

Graph the rational function.f(x) =6- 2x +1Start by drawing the vertical and horizontal asymptotes. Then plot two points on each piece of the graph. Finally, click on the graph-a-function button.Yes

Answer 1

looking at the function

`f(x)=(6)/(-2x+1)`

To get the horizontal asymptote, we look at the degree of the numerator and the degree of the denominator.

For the numerator, the degree of the numerator is zero because

`\begin{gathered} 6* x^o \\ 6*1=6 \end{gathered}`

But for the denominator

`\begin{gathered} \text{Looking at } \\ -2x^{} \\ We\text{ s}e\text{e }x^1. \end{gathered}`

Since the degree of the numerator is less than the degree of the denominator, then the horizontal asymptote is on the x-axis, that is y = 0

To find the vertical asymptote, we set the denominator of the function to be equal to zero. This becomes

`\begin{gathered} -2x+1=0 \\ -2x=-1 \\ x=(-1)/(-2) \\ \\ x=(1)/(2) \end{gathered}`

Therefore, the vertical asymptote is

`x=(1)/(2)`

Now, let's do the graph

Below is the graph for the vertical asymptote, horizontal asymptote, and the function

The red line is the horizontal asymptote,

the blue line is the vertical asymptote

the green curve is the function