Question

1. # Determine Algebraically Whether The Function Is Even, Odd, Or Neither Even Nor Odd. F(X) = 3X2 – 1

Algebra is an important tool for understanding the properties of various functions. In particular, it is useful for determining whether a function is even, odd, or neither even nor odd. It is especially important to understand these properties in order to simplify complicated equations and solve problems related to them. This article will discuss how you can use algebra to determine whether the function F(x) = 3×2 – 1 is even, odd, or neither even nor odd. We’ll walk through each step of the process in detail so that you can be sure you’re getting the right answer every time.

## What is an Even Function?

In mathematics, even functions are functions that are equal to their own inverse when reflected across the y-axis. In other words, they are symmetric with respect to the y-axis. Even functions have the following properties:

– They have a point of symmetry at the origin (x=0, y=0).
– Their graph is symmetric with respect to the y-axis.
– The function’s values for negative input values are equal to the function’s values for positive input values, but with the opposite sign.

Some examples of even functions include: x^2, |x|, and cos(x).

## What is an Odd Function?

An odd function is a function that produces an output that is the opposite of what would be expected based on the input. For example, if you were to input a positive number into an odd function, the output would be negative. Odd functions are important in mathematics and physics because they can be used to create wave-like patterns.

## How to Determine If a Function Is Even, Odd, or Neither

When determining whether a function is even, odd, or neither, there are a few things to keep in mind. First, recall that a function is even if f(x) = f(-x), and a function is odd if f(x) = -f(-x). So, to determine if a function is even, odd, or neither, we need to plug in different values for x and see what happens.

Let’s take a look at the function f(x) = x – 3. If we plug in x = 2, then we get f(2) = 2 – 3 = -1. But if we plug in x = -2, then we get f(-2) = -2 – 3 = -5. Since f(2) does not equal f(-2), this means that the function is not even.

Now let’s look at the same function and see if it’s odd. Again, we’ll plug in different values for x and see what happens. If we plug in x = 2, then we get f(2) = 2 – 3 = -1. But when we plug in x=-2, we get f(-2)= (-2)- 3=-5. Since these two values are equal (f(2)=f(-2)), this means that the function is odd!

## The Function F(x) = 3x^2 – 1

When determining whether a function is even, odd, or neither, we must first look at the function’s definition. In this case, the function F(x) = 3x^2 – 1.

We can see that the function is defined in terms of x^2, which is always positive. Therefore, the function will always be positive as well.

Now, let’s take a look at the function’s graph:

From looking at the graph, we can see that the function is symmetric about the y-axis. This means that it is an even function.

## Conclusion

In conclusion, this function is neither even nor odd since it contains a squared term and an x-term with a coefficient of 1. Even functions must be symmetrical around the y-axis so that f(x) = f(-x), while odd functions must have negative symmetry around the origin so that f(x) = -f(-x). Since the equation for F(X) does not meet either of these criteria, it can be determined algebraically to be neither even nor odd.