Question

is the function a polynomial function?

(f(x) = 3x + 2x^2)

• no
• yes

Explanation:

Define a polynomial function

Using the Polynomial Functions knowledge point
A polynomial function is a function of the form:

$$f(x) = a_n x^n + a_{n-1} x^{n-1} + \dots + a_1 x + a_0$$

where the exponents \(n, n-1, \dots\) are non-negative integers, and the coefficients \(a_i\) are real numbers.

Analyze the given function

Using the Polynomial Functions knowledge point
The given function is:

$$f(x) = 3x + 2x^2$$

We can rewrite this in standard form:

$$f(x) = 2x^2 + 3x$$

The exponents of \(x\) are \(2\) and \(1\), which are both non-negative integers. The coefficients are \(2\) and \(3\), which are real numbers. Therefore, the function is a polynomial function.

Answer:

• No
• Yes (Correct answer)