Question

topic 5 lesson 2: practice level 2: fill in the blanks/answer the questions 1. what is end behavior?

Explanation:

In mathematics, end - behavior refers to the behavior of the graph of a function as \(x\) approaches positive infinity (\(x
ightarrow+\infty\)) or negative infinity (\(x
ightarrow-\infty\)). For polynomial functions \(y = a_nx^n+\cdots+a_0\), the end - behavior is determined by the leading term \(a_nx^n\). If \(n\) is even and \(a_n> 0\), as \(x
ightarrow\pm\infty\), \(y
ightarrow+\infty\); if \(n\) is even and \(a_n < 0\), as \(x
ightarrow\pm\infty\), \(y
ightarrow-\infty\); if \(n\) is odd and \(a_n>0\), as \(x
ightarrow+\infty\), \(y
ightarrow+\infty\) and as \(x
ightarrow-\infty\), \(y
ightarrow-\infty\); if \(n\) is odd and \(a_n < 0\), as \(x
ightarrow+\infty\), \(y
ightarrow-\infty\) and as \(x
ightarrow-\infty\), \(y
ightarrow+\infty\).

Answer:

In mathematics, end - behavior describes how the graph of a function behaves as \(x\) approaches positive or negative infinity. For polynomial functions, it is determined by the degree and the sign of the leading coefficient.