Determine whether the function is even, odd, or neither. Then determine whether the function’s graph is symmetr

Determine whether the function is even, odd, or neither. Choose the correct answer below.
even
neither
odd
Determine whether the graph of the function is symmetric with respect to the -axis, the origin, or neither. Select
y-axis
neither
origin

Question

Determine whether the function is even, odd, or neither. Then determine whether the function’s graph is symmetr

Determine whether the function is even, odd, or neither. Choose the correct answer below.
even
neither
odd
Determine whether the graph of the function is symmetric with respect to the

-axis, the origin, or neither. Select
y-axis
neither
origin

UpStudy AI · Accepted Answer

Analyze the function $$ g(x)=x^{6}-3x $$ to determine whether it is even, odd, or neither.
Function by following steps:
- step0: Determine if even, odd or neither:
  $$g\left(xight)=x^{6}-3x$$
- step1: Use substitution:
  $$g\left(-xight)=\left(-xight)^{6}-3\left(-xight)$$
- step2: Simplify:
  $$g\left(-xight)=x^{6}+3x$$
- step3: The function is neither even nor odd:
  $$	extrm{Neither even nor odd}$$
Analyze the function $$ g(x)=x^{6}-3x $$ to determine whether its graph is symmetric with respect to the $$ y $$-axis, the origin, or neither.
Testing for symmetry by following steps:
- step0: Testing for symmetry about the x-axis:
  $$g\left(xight)=x^{6}-3x$$
- step1: Use substitution:
  $$-g=x^{6}-3x$$
- step2: Change the signs both sides:
  $$g=-x^{6}+3x$$
- step3: The graph of $$g\left(xight)=x^{6}-3x$$ is not symmetry with respect to the x-axis$$:$$
  $$	extrm{Not symmetry with respect to the x-axis}$$
The function $$ g(x) = x^{6} - 3x $$ is neither even nor odd. The graph of the function is not symmetric with respect to the $$ y $$-axis or the origin.
The function $$ g(x) = x^{6} - 3x $$ is neither even nor odd. Its graph is not symmetric with respect to the $$ y $$-axis or the origin.

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