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Chapter 2: Problem 1

Determine which functions are polynomial functions. For those that are, identify the degree. $$f(x)=5 x^{2}+6 x^{3}$$

Short Answer

Expert verified
The function \(f(x) = 5 x^{2} + 6 x^{3}\) is a polynomial function of degree 3.

Step by step solution

01

Identify the function

We are given a function \(f(x) = 5 x^{2} + 6 x^{3}\).
02

Check if the function is polynomial

In the given function, the variables are only raised to non-negative integer powers (here 2 and 3) and we are only using operations of addition and multiplication. So, the given function \(f(x) = 5 x^{2} + 6 x^{3}\) is a polynomial function.
03

Identify the degree of the polynomial

The degree of a polynomial is the highest power of the variable. Looking at the function, \(f(x) = 5 x^{2} + 6 x^{3}\), we can see the highest power of the variable \(x\) is 3. Therefore, the degree of the polynomial \(f(x) = 5 x^{2} + 6 x^{3}\) is 3.

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Most popular questions from this chapter

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{3 x-7}{x-2}$$

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