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

Brief Explanations:

In mathematics, end - behavior refers to the behavior of the graph of a function as (x) approaches positive infinity ((x\rightarrow+\infty)) or negative infinity ((x\rightarrow-\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\rightarrow\pm\infty), (y\rightarrow+\infty); if (n) is even and (a_n < 0), as (x\rightarrow\pm\infty), (y\rightarrow-\infty); if (n) is odd and (a_n>0), as (x\rightarrow+\infty), (y\rightarrow+\infty) and as (x\rightarrow-\infty), (y\rightarrow-\infty); if (n) is odd and (a_n < 0), as (x\rightarrow+\infty), (y\rightarrow-\infty) and as (x\rightarrow-\infty), (y\rightarrow+\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.