How do you find the end behavior of #g(x) = 2x^4 +1#?

To find the end behavior of the function ( g(x) = 2x^4 + 1 ):

1. Degree of Polynomial: Note that the highest power of ( x ) in the polynomial is 4. This indicates that the polynomial is of degree 4.

2. Leading Coefficient: The leading coefficient is the coefficient of the term with the highest power of ( x ), which is ( 2 ) in this case.

3. End Behavior:

   • For even-degree polynomials with a positive leading coefficient (as in this case), both ends of the graph tend upwards.
   • As ( x ) approaches positive infinity (( +\infty )), the function grows without bound.
   • As ( x ) approaches negative infinity (( -\infty )), the function also grows without bound.

Therefore, the end behavior of the function ( g(x) = 2x^4 + 1 ) is as follows:

• As ( x ) approaches positive infinity, ( g(x) ) increases without bound.
• As ( x ) approaches negative infinity, ( g(x) ) increases without bound.