12 basic functions

Identity

f(x)=x
D: (-∞, ∞) R: (-∞,∞)
increasing: (-∞, ∞) decreasing: none
odd function
not bounded
extrema: none
end behavior -∞ as -∞, ∞ as ∞

cubing

f(x)= x^3
D: (-∞,∞) R: (-∞,∞)
Increasing: (-∞,∞) decreasing: none
odd function
Extrema: none
End behavior -∞ as -∞, ∞ as ∞

square root

f(x)=√x
D: [0,∞) R: [0,∞)
Increasing: [0, ∞) decreasing: none
not symmetrical
Extrema: none
End Behavior: none as -∞, ∞ as ∞

natural logarithm

f(x)=ln(x)
D: (0,∞) R: (-∞,∞)
not symmetrical
Extrema: none
End behavior: none as -∞, ∞ as ∞

Cosine

f(x)= cos(x)
D: (-∞,∞) R: [-1, 1]
increases and decreases
even function
End behavior: stays between -1 and 1

Greatest integer

f(x)=int(x) or f(x)= [|x|]
D: (-∞,∞) R: Z
not symmetrical
Extrema: none
End behavior: -∞ as -∞, ∞ as ∞

squaring

F(x)= x^2
D: (-∞,∞) R: [0,∞)
increases and decreases
even function
Extrema: absolute min
End behavior: ∞ as -∞, ∞ as ∞

Reciprocal

f(x)= 1/x
D: (-∞,0) u (0, ∞) R: (-∞,0) u (0, ∞)
decreases
odd function
Extrema: none
End behavior: 0 as -∞, 0 as ∞

Exponential

f(x)= e^x
D: (-∞,∞) R: (0, ∞)
increases
not symmetrical
Extrema: none
End behavior: 0 as -∞, ∞ as ∞

Sine

f(x)= sin(x)
D: (-∞, ∞) R: [-1,1]
odd function
Extrema: N/A
End behavior: stays between -1 and 1

Absolute value

f(x)= |x|
D: (-∞,∞) R: [0, ∞)
even function
Extrema: minimum
End behavior: ∞ as ∞, ∞ as -∞

Logistic

f(x)= 1/ 1+ e^-x
D: (-∞,∞) R: (0,1)
not symmetrical
Extrema: none
End behavior 0 as -∞, 1 as ∞