Find the End Behavior y=5-17x^7+9x^10

$y = 5 - 17 x^{7} + 9 x^{10}$

Step 1

Simplify $5 - 17 x^{7} + 9 x^{10}$ .

Move $5$ .

$y = - 17 x^{7} + 9 x^{10} + 5$

Reorder $- 17 x^{7}$ and $9 x^{10}$ .

$y = 9 x^{10} - 17 x^{7} + 5$

Step 2

Identify the degree of the function.

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$9 x^{10} \to 10$

$- 17 x^{7} \to 7$

$5 \to 0$

The largest exponent is the degree of the polynomial.

$10$

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.

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

$9 x^{10}$

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

$9$

Step 5

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

Positive

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.

Rises to the left and rises to the right

Step 8