Question

Match each equation with its graph. $h(x)=5 x^{3}-6 x+2$

   Match each equation with its graph.
$h(x)=5 x^{3}-6 x+2$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 5, Problem 90

Instant Answer

Solved by Expert Cory Kuzinski

07/17/2020

Step 1

The function $h(x)=5 x^{3}-6 x+2$ is a cubic function because the highest power of $x$ is 3. Show more…

Show all steps

lock

Thanks for your feedback!

Match each equation with its graph. $h(x)=5 x^{3}-6 x+2$

Play audio

Feedback

Powered by NumerAI

Cory Kuzinski and 65 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Cubic Functions

Cubic functions are polynomial functions of degree three. They typically have an S-shaped curve with one inflection point and can display up to two turning points. Their behavior is heavily dictated by the leading coefficient and the degree, which affects the overall shape and orientation of the graph.

Leading Coefficient Test

The leading coefficient test is used in graphing polynomial functions to predict the end behavior of the graph. For cubic functions, a positive leading coefficient means the graph falls to negative infinity on the left and rises to positive infinity on the right, while a negative leading coefficient reverses this behavior.

Graphical Features of Polynomial Functions

Understanding the graphical features such as intercepts, turning points, and inflection points is crucial in matching a polynomial equation to its graph. These features help identify the behavior of the function at different intervals and provide insight into how the algebraic expression translates into a visual curve.

Function Transformations

Function transformations, including vertical and horizontal shifts, stretches, and reflections, are important concepts when graphing equations. Although a basic cubic function has a standard shape, coefficients and constant terms in the equation can alter its graph, which is essential in linking an algebraic expression with its corresponding graph.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later