End Behavior of Functions

Describe the end behavior of the function.

•  $as\ x→-∞,\ f(x)\rightarrow-∞$  
   $as\ x→∞,\ f(x)\rightarrow∞$  
  

•  $as\ x→-∞,\ f(x)\rightarrow∞$  
   $as\ x→∞,\ f(x)\rightarrow-∞$  
  

•  $as\ x→-∞,\ f\left(x\right)\rightarrow0$  
   $as\ x→∞,\ f(x)\rightarrow∞$  
  

•  $as\ x→-∞,\ f(x)\rightarrow∞$  
   $as\ x→∞,\ f(x)\rightarrow∞$  
  

Describe the end behavior of the function.

(Keep in mind Horizontal Asymptotes are not usually drawn)

• $as\ x→-∞,\ f(x)\rightarrow∞$
  
  $as\ x→∞,\ f(x)\rightarrow∞$
  

• $as\ x→-∞,\ f(x)\rightarrow\infty$
  
  $as\ x\rightarrow∞,\ f(x)\rightarrow1$

• $as\ x→-∞,\ f(x)\rightarrow-1$
  
  $as\ x→∞,\ f(x)\rightarrow1$

• $as\ x→-∞,\ f(x)\rightarrow1$
  $as\ x→-∞,\ f(x)\rightarrow1$
  

Describe the end behavior of the function.

• $as\ x→-∞,\ f(x)\rightarrow∞$
  $as\ x→∞,\ f(x)\rightarrow-∞$
  

• $as\ x→-∞,\ f(x)\rightarrow-∞$
  $as\ x→∞,\ f(x)\rightarrow-∞$
  

• $as\ x→-∞,\ f(x)\rightarrow2$
  $as\ x→∞,\ f(x)\rightarrow2$
  

• $as\ x→-∞,\ f(x)\rightarrow∞$
  $as\ x→∞,\ f(x)\rightarrow∞$
  

In the above graph complete the following end behavior:
 $as\ x→-∞,\ f(x)=\rightarrow\$  
 $as\ x→∞,\ f(x)=\rightarrow$  

•  $-\infty$  
   $-\infty$  
  

•  $\infty$  
   $-\infty$  

•  $-\infty$  
   $\infty$  

•  $\infty$  
   $\infty$  

In the above graph complete the following end behavior:
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

• -∞
  -∞
• +∞
  -∞
• -∞
  +∞
• +∞
  +∞

Describe the end behavior of the graph.

• x →∞, y→⁻∞ and x →⁻∞,y→⁻∞
• x →∞, y→∞ and x→⁻∞, y→∞
• x →∞, y→∞ and x→⁻∞, y→2
• x →∞,y→2 and x→⁻∞, y→∞

• The end behavior of the graph is x →∞, y→∞ and x→∞, y→⁻∞
• The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→∞
• The end behavior of the graph is x →∞, y→∞ and x→⁻∞, y→0
• The end behavior of the graph is x →∞,y→0 and x→∞, y→⁻∞

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

What is the end behavior of the function f(x) graphed above?

• $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow\infty$
  $as\ x\ \rightarrow\infty,\ f\left(x\right)\ \rightarrow\infty$
  

• $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow0$
  $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$
  

• $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow0$
  $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow0$
  

• $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$
  $as\ x\ \rightarrow-\infty,\ f\left(x\right)\ \rightarrow-\infty$
  

What is the end behavior of h(x)?

• $as\ x\ \rightarrow\ -\infty,\ h\left(x\right)\ \rightarrow\infty$
  $as\ x\ \rightarrow\ \infty,\ h\left(x\right)\ \rightarrow\infty$
  

• $as\ x\ \rightarrow\ -\infty,\ h\left(x\right)\ \rightarrow-\infty$
  $as\ x\ \rightarrow\ \infty,\ h\left(x\right)\ \rightarrow-\infty$
  

• $as\ x\ \rightarrow\ -\infty,\ h\left(x\right)\ \rightarrow\infty$
  $as\ x\ \rightarrow\ \infty,\ h\left(x\right)\ \rightarrow-\infty$
  

• $as\ x\ \rightarrow\ -\infty,\ h\left(x\right)\ \rightarrow-\infty$
  $as\ x\ \rightarrow\ \infty,\ h\left(x\right)\ \rightarrow\infty$