Find the End Behavior f(x)=3x^4


Step 1
The largest exponent is the degree of the polynomial.

Step 2
Since the degree is even, the ends of the function will point in the same direction.
Even

Step 3
Identify the leading coefficient.

The leading term in a polynomial is the term with the highest degree.
The leading coefficient in a polynomial is the coefficient of the leading term.

Step 4
Since the leading coefficient is positive, the graph rises to the right.
Positive

Step 5
Use the degree of the function, as well as the sign of the leading coefficient to determine the behavior.
1. Even and Positive: Rises to the left and rises to the right.
2. Even and Negative: Falls to the left and falls to the right.
3. Odd and Positive: Falls to the left and rises to the right.
4. Odd and Negative: Rises to the left and falls to the right

Step 6
Determine the behavior.
Rises to the left and rises to the right

Step 7


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