Problem 22 Describe the right-hand and left... [FREE SOLUTION]

Chapter 2: Problem 22

Describe the right-hand and left-hand behavior of the graph of the polynomial function. \(f(x)=2 x^{2}-3 x+1\)

Short Answer

Expert verified

The right-hand behavior of the function \(f(x)=2 x^{2}-3 x+1\) is that it increases without limit as x approaches positive infinity. The left-hand behavior of the function is that it also increases without limit as x approaches negative infinity.

Step by step solution

Identify the Degree and Leading Coefficient

First, identify the degree and the leading coefficient. The degree of a polynomial is the highest exponent of its variable. The leading coefficient is the coefficient of the term with the highest degree. In this function, \(f(x)=2 x^{2}-3 x+1\), the degree is 2 and the leading coefficient is 2.

Determine the Right-Hand Behavior

For the right-hand behavior, or limit as x approaches positive infinity, consider the degree and sign of the leading coefficient. If the degree is even and the leading coefficient is positive, the function increases without limit (upwards) as x approaches positive infinity.

Determine the Left-Hand Behavior

For the left-hand behavior, or limit as x approaches negative infinity, again consider the degree and sign of the leading coefficient. If the degree is even and the leading coefficient is positive, the function increases without limit (upwards) as x approaches negative infinity.

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91影视

Describe the right-hand and left-hand behavior of the graph of the polynomial function. \(f(x)=2 x^{2}-3 x+1\)

Short Answer

Step by step solution

Identify the Degree and Leading Coefficient

Determine the Right-Hand Behavior

Determine the Left-Hand Behavior

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