Question

Whether the function is even, odd, or neither
f(x)=3x²+1

Answer 1

Answer: Even

Explanation

Rewrite the +1 at the end as +1x^0

So we really have this function

f(x) = 3x^2 + 1x^0

All of the exponents are even, so the polynomial function is even.

Visually this parabola has symmetry with the y axis which is a trait of any even function.

Answer 2

The function f(x) = 3x² + 1 is an even function.

Step-by-step explanation:

A function is even if and only if it satisfies the property f(x) = f(-x) for all values of x in the domain. Similarly, a function is odd if and only if it satisfies the property f(x) = -f(-x) for all values of x in the domain. In the given function, f(x) = 3x² + 1. To determine if it is even, odd, or neither, we need to check if it satisfies the even or odd properties. Let's substitute -x for x in the function:

f(-x) = 3(-x)² + 1 = 3x² + 1

Since f(-x) is equal to f(x), the function f(x) = 3x² + 1 is an even function.