12 basic functions

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Pre-Calculus

Matrices

11th

Last updated 8:39 PM on 12/9/22
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12 Terms

1
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Identity
f(x)=x
D: (-∞, ∞) R: (-∞,∞)
increasing: (-∞, ∞) decreasing: none
odd function
not bounded
extrema: none
end behavior -∞ as -∞, ∞ as ∞
f(x)=x D: (-∞, ∞) R: (-∞,∞) increasing: (-∞, ∞) decreasing: none odd function not bounded extrema: none end behavior -∞ as -∞, ∞ as ∞
2
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cubing
f(x)= x^3
D: (-∞,∞) R: (-∞,∞)
Increasing: (-∞,∞) decreasing: none
odd function
Extrema: none
End behavior -∞ as -∞, ∞ as ∞
f(x)= x^3 D: (-∞,∞) R: (-∞,∞) Increasing: (-∞,∞) decreasing: none odd function Extrema: none End behavior -∞ as -∞, ∞ as ∞
3
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square root
f(x)=√x
D: [0,∞) R: [0,∞)
Increasing: [0, ∞) decreasing: none
not symmetrical
Extrema: none
End Behavior: none as -∞, ∞ as ∞
f(x)=√x D: [0,∞) R: [0,∞) Increasing: [0, ∞) decreasing: none not symmetrical Extrema: none End Behavior: none as -∞, ∞ as ∞
4
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natural logarithm
f(x)=ln(x)
D: (0,∞) R: (-∞,∞)
not symmetrical
Extrema: none
End behavior: none as -∞, ∞ as ∞
f(x)=ln(x) D: (0,∞) R: (-∞,∞) not symmetrical Extrema: none End behavior: none as -∞, ∞ as ∞
5
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Cosine
f(x)= cos(x)
D: (-∞,∞) R: [-1, 1]
increases and decreases
even function
End behavior: stays between -1 and 1
f(x)= cos(x) D: (-∞,∞) R: [-1, 1] increases and decreases even function End behavior: stays between -1 and 1
6
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Greatest integer
f(x)=int(x) or f(x)= [|x|]
D: (-∞,∞) R: Z
not symmetrical
Extrema: none
End behavior: -∞ as -∞, ∞ as ∞
f(x)=int(x) or f(x)= [|x|] D: (-∞,∞) R: Z not symmetrical Extrema: none End behavior: -∞ as -∞, ∞ as ∞
7
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squaring
F(x)= x^2
D: (-∞,∞) R: [0,∞)
increases and decreases
even function
Extrema: absolute min
End behavior: ∞ as -∞, ∞ as ∞
F(x)= x^2 D: (-∞,∞) R: [0,∞) increases and decreases even function Extrema: absolute min End behavior: ∞ as -∞, ∞ as ∞
8
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Reciprocal
f(x)= 1/x
D: (-∞,0) u (0, ∞) R: (-∞,0) u (0, ∞)
decreases
odd function
Extrema: none
End behavior: 0 as -∞, 0 as ∞
f(x)= 1/x D: (-∞,0) u (0, ∞) R: (-∞,0) u (0, ∞) decreases odd function Extrema: none End behavior: 0 as -∞, 0 as ∞
9
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Exponential
f(x)= e^x
D: (-∞,∞) R: (0, ∞)
increases
not symmetrical
Extrema: none
End behavior: 0 as -∞, ∞ as ∞
f(x)= e^x D: (-∞,∞) R: (0, ∞) increases not symmetrical Extrema: none End behavior: 0 as -∞, ∞ as ∞
10
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Sine
f(x)= sin(x)
D: (-∞, ∞) R: [-1,1]
odd function
Extrema: N/A
End behavior: stays between -1 and 1
f(x)= sin(x) D: (-∞, ∞) R: [-1,1] odd function Extrema: N/A End behavior: stays between -1 and 1
11
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Absolute value
f(x)= |x|
D: (-∞,∞) R: [0, ∞)
even function
Extrema: minimum
End behavior: ∞ as ∞, ∞ as -∞
f(x)= |x| D: (-∞,∞) R: [0, ∞) even function Extrema: minimum End behavior: ∞ as ∞, ∞ as -∞
12
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Logistic
f(x)= 1/ 1+ e^-x
D: (-∞,∞) R: (0,1)
not symmetrical
Extrema: none
End behavior 0 as -∞, 1 as ∞
f(x)= 1/ 1+ e^-x D: (-∞,∞) R: (0,1) not symmetrical Extrema: none End behavior 0 as -∞, 1 as ∞