Problem 23 Describe the right-hand and left... [FREE SOLUTION]

Chapter 2: Problem 23

Describe the right-hand and left-hand behavior of the graph of the polynomial function. \(g(x)=5-\frac{7}{2} x-3 x^{2}\)

Short Answer

Expert verified

The right-hand and left-hand behavior of the graph of the function \(g(x)=5-\frac{7}{2} x-3 x^{2}\) is that it decreases without bound, or approaches negative infinity.

Step by step solution

Identify the Degree and Leading Coefficient

Identify the degree and leading coefficient of the polynomial. They can tell you a lot about the graph. Here, the highest power is 2 (which makes the polynomial a quadratic), and the coefficient of the \(x^2\) term, also known as the leading coefficient, is -3

Determine the End Behavior

Since the degree of this polynomial is even and the leading coefficient is negative. we know that as \(x\) approaches positive infinity, \(g(x)\) will approach negative infinity. Similarly, as \(x\) approaches negative infinity, \(g(x)\) will also approach negative infinity.

Describe the Behavior

Now we have the information to describe the right-hand and left-hand behavior of the function. As \(x\) goes to plus infinity (right-hand side), the function \(g(x)\) decreases without bound. As \(x\) goes to minus infinity (left-hand side), the function \(g(x)\) decreases without bound.

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91影视

Describe the right-hand and left-hand behavior of the graph of the polynomial function. \(g(x)=5-\frac{7}{2} x-3 x^{2}\)

Short Answer

Step by step solution

Identify the Degree and Leading Coefficient

Determine the End Behavior

Describe the Behavior

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