QuestionAnalyze the polynomial $h(x)=x^{6}-3x^{5}-17x^{3}$ and determine its end behavior.

Studdy Solution

STEP 1

Assumptions1. The function is a polynomial function of degree6. . The leading coefficient of the polynomial is1.

STEP 2

The end behavior of a polynomial function can be determined by looking at the degree and the leading coefficient of the polynomial.

STEP 3

The degree of the polynomial $h(x) = x^{6} -3x^{5} -17x^{3}$ is6, which is an even number.

STEP 4

The leading coefficient of the polynomial $h(x)$ is1, which is positive.

STEP 5

For a polynomial with an even degree and a positive leading coefficient, as $x$ approaches positive or negative infinity, $h(x)$ will approach positive infinity.
$\lim{{x \to \infty}} h(x) = \infty$ $\lim{{x \to -\infty}} h(x) = \infty$ This means that the ends of the graph of $h(x)$ will point upwards.

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms