# How do you determine if #g(x) = 4x^2 +2x# is an even or odd function?

By signing up, you agree to our Terms of Service and Privacy Policy

To determine if a function is even or odd, we can analyze its symmetry properties with respect to the y-axis (even functions) or the origin (odd functions).

For a function to be even, it must satisfy the condition: (g(-x) = g(x)) for all (x) in its domain.

For a function to be odd, it must satisfy the condition: (g(-x) = -g(x)) for all (x) in its domain.

Let's apply these conditions to (g(x) = 4x^2 + 2x):

- Even function test: [g(-x) = 4(-x)^2 + 2(-x) = 4x^2 - 2x] [g(x) = 4x^2 + 2x]

As (g(-x) = g(x)), the function satisfies the condition for evenness.

- Odd function test: [g(-x) = 4(-x)^2 + 2(-x) = 4x^2 - 2x] [g(x) = 4x^2 + 2x]

As (g(-x) \neq -g(x)), the function does not satisfy the condition for oddness.

Therefore, (g(x) = 4x^2 + 2x) is an even function.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- What is the domain of #f(x)=tanx#?
- How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x)=(x^2 -1) /(2x^2 + 3x-2)#?
- How do you find the vertical, horizontal or slant asymptotes for #g(x)=5^x#?
- How do you find #f^-1(x)# given #f(x)=(x-3)^2+7#?
- How do you find the asymptotes for #(3x^2+x-4) / (2x^2-5x)#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7