Answer:
See below.
Step-by-step explanation:
For a rational function, the equation is [tex]\displaystyle \large{f(x)=\frac{a}{b(x-c)}+d}[/tex] where:-
- c is horizontal shift.
- d is vertical shift.
- a/b determines how wide or narrow the graph is.
- x = c is a vertical asymptote.
- y = d is a horizontal asymptote.
We are given a function [tex]\displaystyle \large{f(x)=\frac{1}{x}-1}[/tex] . Examine the function, we know that:-
- .The graph has no horizontal shift as c = 0.
- The graph has the vertical shift which is -1. Therefore d = -1
- x = 0 is our vertical asymptote.
- y = -1 is our horizontal asymptote.
Additional Info
- Asymptote line is a line that the graph tends to approach but never intersects.
From the information we have, first - draw both vertical asymptote and horizontal asymptote to make it easier to draw a graph.
Then draw a rational function’s graph as it tends to 0 when x = 0 and -1 when x tends to both sides of infinity.
You should receive a graph below that I made, see the attachment. The purple line represents the horizontal asymptote and y-axis is our vertical asymptote.
If you have any questions, do not hesitate to ask in comment!
