Answer:
Step-by-step explanation:
The absolute value function prevents the expression from being a polynomial. The degree of 3 in y^3 is an odd number so that polynomial function will not be even.
Answer:
The equation [tex]y=x^3[/tex] is not an equation of a simple , even polynomial function.
Step-by-step explanation:
Even function : A function is even when its graph is symmetric with respect to y-axis.
Algebrically , the function f is even if and only if
f(-x)=f(x) for all x in the domain of f.
When the function does not satisfied the above condition then the function is called non even function.
f(x)[tex]\neq[/tex] f(-x)
Now , we check given function is even or not
A. y= [tex]\mid x\mid[/tex]
If x is replaced by -x
Then we get the function
f(-x)=[tex]\mid -x \mid[/tex]
f(-x)=[tex]\mid x \mid[/tex]
Hence, f(-x)=f(x)
Therefore , it is even polynomial function.
B. [tex]y=x^2[/tex]
If x is replace by -x
Then we get
f(-x)=[tex](-x)^2[/tex]
f(-x)=[tex]x^2[/tex]
Hence, f(-x)=f(x)
Therefore, it is even polynomial function.
C. [tex]y=x^3[/tex]
If x is replace by -x
Then we get
f(-x)=[tex](-x)^3[/tex]
f(-x)=[tex]-x^3[/tex]
Hence, f(-x)[tex]\neq[/tex] f(x)
Therefore, it is not even polynomial function.
D.[tex]y= -x^2[/tex]
If x is replace by -x
Then we get
f(-x)= - [tex](-x)^2[/tex]
f(-x)=-[tex]x^2[/tex]
Hence, f(-x)=f(x)
Therefore, it is even polynomial function.
Answer: C. [tex]y=x^3[/tex] is not simple , even polynomial function.
