## How do you find the horizontal asymptote of the graph of f?

**Finding Horizontal Asymptotes of Rational Functions**

- If both polynomials are the same degree, divide the coefficients of the highest degree terms.
- If the polynomial in the numerator is a lower degree than the denominator, the x-axis (y = 0) is the
**horizontal asymptote**.

## Can the graph of y f/x intersect a horizontal asymptote?

Question: **Can the graph of y** = **f** (**x**) **intersect a horizontal asymptote**? Question: How many **horizontal asymptotes can the graph of y** = **f** (**x**) have? Answer: Just 2, corresponding to the case that limx→∞ **f** (**x**) = L1 and limx→∞ **f** (**x**) = L2 and L1 = L2.

## How do you find the horizontal asymptote of an equation?

Another way of **finding** a **horizontal asymptote** of a rational function: Divide N(x) by D(x). If the quotient is constant, then y = this constant is the **equation** of a **horizontal asymptote**.

## How many horizontal asymptotes can a rational function have?

A **rational function can have** at most one **horizontal** or oblique **asymptote**, and **many** possible vertical **asymptotes**; these **can** be calculated.

## What is the horizontal asymptote?

**Horizontal asymptotes** are **horizontal** lines the graph approaches. If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the **horizontal asymptote** is the x-axis (y = 0). If the degree of the numerator is bigger than the denominator, there is no **horizontal asymptote**.

## How do you find vertical and horizontal asymptotes?

The **vertical asymptotes** will occur at those values of x for which the denominator is equal to zero: x2 − 4=0 x2 = 4 x = ±2 Thus, the graph will have **vertical asymptotes** at x = 2 and x = −2. To find the **horizontal asymptote**, we note that the degree of the numerator is one and the degree of the denominator is two.

## Why does a graph cross the horizontal asymptote?

For example, if you have the function y=1×2−1 set the denominator equal to zero to find where the vertical **asymptote is**. Because of this, **graphs can cross** a **horizontal asymptote**. A rational function **will** have a **horizontal asymptote** when the degree of the denominator **is** equal to the degree of the numerator.

## How many horizontal asymptotes can there be?

A function can have at most **two** different horizontal asymptotes.

## How do you find the horizontal asymptote using limits?

A function f(x) will have the **horizontal asymptote** y=L if either limx→∞f(x)=L or limx→−∞f(x)=L. Therefore, to **find horizontal asymptotes**, we simply evaluate the **limit** of the function as it approaches infinity, and again as it approaches negative infinity.

## Can a rational function have both vertical and horizontal asymptotes?

Note that a graph can **have both** a **vertical** and a **slant asymptote**, or **both** a **vertical and horizontal asymptote**, but it CANNOT **have both** a **horizontal** and **slant asymptote**.

## Do square root functions have horizontal asymptotes?

So, that’s one explanation of why **square root functions have** no **asymptote**. You can think of a **square root function** as the inverse of a quadratic (i.e. **take** a quadratic, flip it in the diagonal line and then only keep the top half). A quadratic **has** no **asymptotes** because it is a 2nd degree polynomial.

## Why can a function have more than two vertical asymptotes?

1 Answer. Generally, a **function has** a **vertical asymptote** at x when it **can** be expressed as: f(x)=ag(x)∣a≠g(x) and g(x)=0, the simplest example of which is 1x. For a **function** to **have** infinitely many **vertical asymptotes** there must be infinitely many values of x for which g(x)=0.