Question

How do you find vertical, horizontal and oblique asymptotes for `f(x) = (5x-15 )/ (2x+14)`?

Answer 1

Vertical asymptote = x = -7, Horizontal asymptote = y = 5/2, no oblique asymptotes.

Explanation:

An ASYMPTOTE is a line that approches a curve, but NEVER meets it.

To find the vertical asymptote , put the denominator = 0 (because 0 cannot divide any number) and solve.

Given below is the step-by-step walk through

The curve can never touch x = -7, thus making it the vertical asymptote.

To find the horizontal asymptote , compare the degree of the expressions in the numerator and the denominator.
Here, the degree of the numerator = 1 and the degree of the denominator = 1.
Since the degrees are equal, the horizontal asymptote

`y = ("numerator's leading coefficient)"/"(denominator's leading coefficient")`

`y = 5/2`

The oblique asymptote is a line of the form y = mx + c.
In other words,
degree of numerator = degree of denominator + 1
Here, the degree of the numerator = degree of the denominator.
Therefore, the given function has no oblique asymptotes.

The graph for the function is given below:
graph{(5x-15)/(2x+14) [-35.9, 37.16, -15.5, 21.04]}![enter image source here]