Question

Which graph represents the function f(x)=

(x)=3-12
X
5
4
3
2-
1
-5 -4 -3 -2 -1
1 2 3
4 5
941

Answer 1

See below.

Explanation:

For a rational function, the equation is
`\displaystyle \large{f(x)=(a)/(b(x-c))+d}` 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
`\displaystyle \large{f(x)=(1)/(x)-1}` . 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!