0

# Determine whether the graph of the given function f(x) = 4x^3 is symmetric with respect to the y-axis, symmetric with respect to the origin, or neither.

Determine whether the graph of the given function f(x) = 4x^3 is symmetric with respect to the y-axis, symmetric with respect to the origin, or neither.

### 2 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
5.0 5.0 (3 lesson ratings) (3)
0
f(x) = 4x^3

f(-x) = 4(-x)^3 = -4x^3 = -f(x)

So the f is symmetric with respect to the origin and "odd".

But f(-x) ≠ f(x) so f is not symmetric with respect to the y-axis so is not "even".

[N.B.: Any circle x^2 + y^2 = r^2 is symmetric to any line through the origin: it's even, odd, and its own inverse.]
Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
0
f(x ) = 4X^3

f( 1) = 4 ( 1 ) ^3 = 4

f ( -1 ) = 4 (-1)^3 = -4

It is not Symmetric with respect to Y- axis : Because f(1) ≠ f( -1)

It is Symmetric w.r.t origin because  :   f( 1) = - f( -1)