Algebra Examples

$- x^{4}$

Step 1

Write $- x^{4}$ as a function.

$f (x) = - x^{4}$

Step 2

The largest exponent is the degree of the polynomial.

$4$

Step 3

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

Even

Step 4

Identify the leading coefficient.

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

$- x^{4}$

The leading coefficient in a polynomial is the coefficient of the leading term.

$- 1$

Step 5

Since the leading coefficient is negative, the graph falls to the right.

Negative

Step 6

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 7

Determine the behavior.

Falls to the left and falls to the right

Step 8