Arrow notation

Definition

Arrow notation is a way to describe the behavior of functions as the input approaches a particular value or infinity. It is often used to express limits and asymptotic behavior.

5 Must Know Facts For Your Next Test

1. Arrow notation, such as $x \rightarrow \infty$, indicates that $x$ approaches infinity.
2. It can be used to describe horizontal asymptotes, e.g., $f(x) \rightarrow L$ as $x \rightarrow \infty$ means the function approaches $L$ as $x$ goes to infinity.
3. Vertical asymptotes can be described using arrow notation by indicating that $f(x)$ approaches infinity or negative infinity as $x$ approaches a specific value.
4. Arrow notation helps in understanding end behavior of polynomial and rational functions.
5. It is essential for expressing limits in calculus, but its understanding starts in algebra when studying rational functions.

Review Questions

• What does it mean when we write $f(x) \rightarrow 0$ as $x \rightarrow -\infty$?
• How would you use arrow notation to describe the behavior of a function near a vertical asymptote?
• Explain what is meant by $f(x) \rightarrow L$ as $x \rightarrow c^+$.

Related terms

Asymptote: A line that a graph approaches but never touches.

End Behavior: The behavior of the graph of a function as \( x \) approaches positive or negative infinity.

Limit: \( f(x) \) approaches a particular value \( L \) as \( x \) approaches some value \( c \).