Question

What is the graph of the function f(x) = the quantity of x plus 5, all over x minus 2

Answer 1

I attached a plot that you can use as a model.

You should understant that to draw this graph you should:

1) built a table with several values of x and f(x)

2) determine the domain (all the real numbers except x = 2

3) determine the range (all the real numbers)

4) find local maxima and minima

5) find the limif of f(x) when x goes to 0 by the left and by the right (+∞ and - ∞)

6) find the roots of the function (calculate x when y = 0)

7) find the y-intercepts (calculate x when y = 0)

Answer 2

The graph of
`(x+5)/(x-2)` is shown below

The horizontal asymptote is the value of x that makes the denominator = 0

x - 2 = 0
x = 2

The function has a horizontal asymptote because the polynomial degree of both numerator and denominator is the same; both of degree one.
The horizontal asymptote is the coefficient of the leading polynomial, so it's
y = 1