graph the function y = 2x^4 + 4x^3 = 2x^3(x + 2) by identifying the domain and any symmetries, finding the…

graph the function y = 2x^4 + 4x^3 = 2x^3(x + 2) by identifying the domain and any symmetries, finding the derivatives y and y, finding the critical points and identifying the functions behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and plotting any key points such as intercepts, critical points, and inflection points. then find coordinates of absolute extreme points, if any. find the domain of the function. the domain is . (type your answer in interval notation.) identify any symmetries. choose the correct answer below. a. the function is an even function that is symmetric about the y - axis. b. the function is an odd function that is symmetric about the y - axis. c. the function is an even function that is symmetric about the origin. d. the function is an odd function that is symmetric about the origin.

graph the function y = 2x^4 + 4x^3 = 2x^3(x + 2) by identifying the domain and any symmetries, finding the derivatives y and y, finding the critical points and identifying the functions behavior at each one, finding where the curve is increasing and where it is decreasing, finding the points of inflection, determining the concavity of the curve, identifying any asymptotes, and plotting any key points such as intercepts, critical points, and inflection points. then find coordinates of absolute extreme points, if any. find the domain of the function. the domain is . (type your answer in interval notation.) identify any symmetries. choose the correct answer below. a. the function is an even function that is symmetric about the y - axis. b. the function is an odd function that is symmetric about the y - axis. c. the function is an even function that is symmetric about the origin. d. the function is an odd function that is symmetric about the origin.

Answer

Explanation:

Step1: Determine domain

Polynomial functions have no restrictions on input values. So the domain of $y = 2x^{4}+4x^{3}=2x^{3}(x + 2)$ is all real - numbers.

Step2: Check for symmetry

Let $f(x)=2x^{4}+4x^{3}$. Then $f(-x)=2(-x)^{4}+4(-x)^{3}=2x^{4}-4x^{3}$. Since $f(-x)\neq f(x)$ and $f(-x)\neq - f(x)$, the function is neither even nor odd. But we can check the general rules for symmetry. An even function satisfies $f(x)=f(-x)$ (symmetry about y - axis) and an odd function satisfies $f(-x)=-f(x)$ (symmetry about the origin).

Answer:

The domain is $(-\infty,\infty)$ No correct option for symmetry.