Question

question 2 (1 point)determine the symmetry and domain of the polynomial function.$f(x) = x^3 + 6x^2 + 8x$□ domain: all real numbers□ symmetry: odd□ symmetry: none□ domain: x>-4

Explanation:

Step1: Find the function's domain

Polynomials accept all real $x$.
Domain: All real numbers

Step2: Test for odd symmetry

Compute $f(-x)$:
$f(-x) = (-x)^3 + 6(-x)^2 + 8(-x) = -x^3 + 6x^2 - 8x$
Test $f(-x) = -f(x)$:
$-f(x) = -(x^3 + 6x^2 + 8x) = -x^3 -6x^2 -8x$
$f(-x)
eq -f(x)$, so not odd.

Step3: Test for even symmetry

Test $f(-x) = f(x)$:
$f(x) = x^3 +6x^2 +8x$, $f(-x) = -x^3 +6x^2 -8x$
$f(-x)
eq f(x)$, so no even symmetry.

Answer:

Domain: All Real Numbers
Symmetry: None