+155 Given this function: f(x) =3/[x+3] -9
explain how you'd identify the vertical asymptote of the function without graphing.
identify the horizontal asymptote of the function writing the entire equation
also can you explain how to identify the horizontal asymptote of the function without graphing.
+128475 f(x) = 3 / { x + 3] - 9
The vertical asymptote is the value of x that makes the denominator = 0
So....
x + 3 = 0
x = - 3 ⇒ vertical asymptote
To find the horizontal asymptote.....note that 3/ [ x +3 ] is a lower power polynomial / higher power polynomial
When we have this situation, the horizontal asymptote is y = 0
However ..... the "-9" at the end actually shifts this horizontal aymptote DOWN by 9 units
So....the horizontal asymptote is y = - 9
Here's the graph : https://www.desmos.com/calculator/93af4udovt
