Answer to Question #92910 in Algebra for Idongesit Effiong

Question

Define the following with two examples
Zeros function
Even function
Odd function
Heaviside function
Greatest integer function
Absolute function
Identity function
Constant function
Periodic function

Answer 1

1) Zero function: This is a function equal to zero on every point of its domain ($y=0, y=0(x+1)$ );

2) Even function: For every x of this type of function $f(-x)=f(x)$ ($y=x^2, y=cos(x))$

3) Odd function: For every x of this type of function $f(-x)=-f(x)$ ($y=x^3, y=sin(x)$)

4) Heaviside function: This is a unit step function $H(x):=\frac{d}{dx}max(x,0)$ ($H(x)=\frac{1}{2}+\frac{1}{2}sgn(x), H(x)=1_{[0, infinity)}(x)$)

5) Greatest integer function: The Greatest integer function is defined as the largest integer which is less than or equal to x ($y=[x], y=\frac{1}{2}[x]$)

6) Absolute number: This is a positive number for positive x and the opposite number for a negative x ($y=\mid{x}\mid, y=\mid{x+1}\mid)$

7) Identity function: This is actually the same value that was used as an argument ($y=x$)

8) Constant function: This is the function with the same value for every argument x ($y=3, y=3.14$)

9) Periodic function: For every x of this function $f(x)=f(x+a)$, where a is a non-zero real number or period ($y=sin(x), y=cos(x)$)