This **article aims to determine whether the given statement is true or false**. The statement is, “**The graph of a rational function may intersect a horizontal asymptote**.” This article uses the **concept of horizontal asymptote** of the **rational function**.

A **horizontal asymptote** is **horizontal line** that is not part of the graph of a function but leads it for $ x $ values **“far” right and “far” left.** The graph may intersect it, but eventually, for large enough or small enough values of $ x $, **graph would get closer and closer to asymptote** without touching it. **Horizontal asymptote** is a special case of an **oblique asymptote.**

**Horizontal asymptote of rational function** can be find by looking at degrees of the **numerator and denominator.**

If $ N $ is the degree in the **numerator** and $ D, $ is the degree in the **denominator**.

-$ N < D $, then the **horizontal asymptote** is $ y = 0$.

-$ N = D $, then the **horizontal asymptote** is $ y = ratio\: of\: leading\: coefficients $.

-$ N > D $, then there is no** horizontal asymptote.**

**Expert Answer**

The **statement is true.** It is possible that **graph of a rational function can cross a horizontal asymptote.**

**Horizontal asymptote of a rational function** can find by observing at the degrees of the **numerator and denominator.**

-The** degree of the numerator is less than the degree of the denominator:** **horizontal asymptote** at

-$ y = 0 $

-The** degree of the numerator is greater than the degree of the denominator** by one: no horizontal asymptote; **oblique asymptote.**

-The** degree of the numerator** is equal to the **degree of the denominator:** the **horizontal asymptote** in the **ratio of the leading coefficients.**

**Numerical Result**

The **statement is true.** It is possible that the **graph of a rational function can cross a horizontal asymptote.**

**Example**

**True or False: Graph of a rational function $ R $ never crosses a vertical asymptote. True or False: Graph of a rational function $ R $ never crosses a horizontal asymptote. True or False: Graph of a rational function $ R $ never crosses an oblique asymptote.**

**Solution**

**All statements are true.**

An **asymptote** is a line along which the values of a **function approaches** but never reach, such that one or both of the $ x $ or $ y $ **coordinates tend to positive or negative infinity**. Therefore, the **graph of a rational function** $ R $ never **intersects** any of its** asymptotes.**