Lesson Funky Functions

These are Examples of Common Functions
Direct Function:
graph( 600, 600, -10, 10, -10, 10, 1.5x )

Domain: all reals
Range: all reals
Constant Function:
graph( 600, 600, -10, 10, -10, 10, 2 )

Domain: all reals
Range: f(x) = 2
Inverse Function: f(x) = 1/x
graph( 600, 600, -10, 10, -10, 10, 1/x )

Domain: x > 0 and 0 > x <====(0)====> Not Equal To Zero
Range: y > 0 and 0 > y <====(0)====} Not Equal To Zero
Rational Function: f(x) = (x - 1)/(x + 1)
graph( 600, 600, -10, 10, -10, 10, (x - 1)/(x + 1) )

Domain: x > -1 and -1 > x <====(-1)====> Not Equal To Negative One
Range: y > 1 and 1 > y <====(1)====> Not Equal To One
Trig Function:
graph( 600, 600, -10, 10, -10, 10, sin(x), 3*cos(x), sin(x)/cos(x) )

f(x) = sin(x)
Domain: all reals
Range: 1 >= x >= -1

f(x) = 3cos(x)
Domain: all reals
Range: 3 >= x >= -3

f(x) = tan(x)
Domain: all reals excluding: +-

/2 +

k .... where 'k' is any integer
Range: all reals
Quadratic Function:
graph( 600, 600, -10, 10, -10, 10, x^2 - 10 )

Domain: all reals
Range: y >= -10

Cubic Function:
graph( 600, 600, -10, 10, -10, 10, x^3 - x^2 + 2 )

Domain: all reals
Range: all reals
Quartic Function:
graph( 600, 600, -10, 10, -10, 10, x^4 - 4x^2 + 1 )

Domain: all reals
Range: y >= -3

Quintic Function:
graph( 600, 600, -10, 10, -12, 12, (x + 3)(x - 2)(x + 1)(x + 2)(x - 1) )

Domain: all reals
Range: all reals
*Just for Fun*
ABSOLUTE VALUED GRAPHS
f(x) = |x^2 - 10|
graph( 600, 600, -10, 10, -10, 10, sqrt((x^2 - 10)^2) )

f(x) = |tan(x)|
graph( 600, 600, -10, 10, -10, 10, sqrt((sin(x)/cos(x))^2) )

f(x) = |sin(x)|
graph( 600, 600, -10, 10, -10, 10, sqrt((sin(x))^2) )

f(x) = |(x + 3)(x - 2)(x + 1)(x + 2)(x - 1)|
graph( 600, 600, -10, 10, -12, 12, sqrt(((x + 3)(x - 2)(x + 1)(x + 2)(x - 1))^2) )

f(x) = |sin(x) + x|
graph( 600, 600, -10, 10, -10, 10, sqrt((sin(x) + x)^2) )