Question

Determine whether the function f(x)=4x^3 is even or odd

Answer 1

Answer:

Step-by-step explanation:

Answer:

odd function

Explanation:

   To determine if a function f(x) is even/odd consider the following.

   • If f(x) = f( -x) , then f(x) is even

   Even functions are symmetrical about the y-axis.

   • If - f(x) = f(-x) , then f(x) is odd

   Odd functions have symmetry about the origin.

   Test for even function

   f(−x)=4(−x)3=−4x3≠f(x)

   Since f(x) ≠ f( -x) , then f(x) is not even

   Test for odd function

   −f(x)=−(4x3)=−4x3=f(−x)

   Since - f(x) = f( -x) , then f(x) is odd

   graph{4x^3 [-10, 10, -5, 5]}

 

Answer 2

Answer:

f(x) is an odd function

Step-by-step explanation:

Determine whether the function f(x)=4x^3 is even or odd

$f(x)= 4x^3$

To check whether f(x) is even then f(-x)= f(x)

To check whether f(x) is odd then f(-x)=-f(x)

Plug in x with -x and check whether it is odd or even

$f(x)= 4x^3$

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

f(-x) is not equal to f(x). So f(x) is not an even function

$f(x)= 4x^3$

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

f(-x) =-f(x)

So it is an odd function