Question

Tell whether the function f(x) = -x^3 + 7x + 4 is an even or odd function, and describe its symmetry.

a) even: symmetric with respect to y-axis

b) odd: symmetric with respect respect to the x-axis

c) odd: symmetric with respect to the origin

d) neither even nor odd: not symmetric

Answer 1

Please help

Answer 2

To determine whether a function is even or odd, we need to find f(-x) and -f(x). If f(x)=f(-x), then the function is even. If -f(x)=f(-x), then the function is odd. \[f(x)=-x^3+7x+4\]\[f(-x)=x^3-7x+4\]\[-f(x)=x^3-7x-4\]Since the function meets neither of the criteria, it is neither odd nor even. Symmetry can be determined by comparing f(x) and f(-x) for symmetry about the y axis, -f(x) and f(x) for symmetry about the x-axis, and -f(x) and f(-x) for symmetry about the origin. Since the function fails all these tests as well, we know the function has no symmetry. So it is neither even nor odd and it has no symmetry.

Answer 3

Thank you sooo much!!

Answer 4

No problem =)