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PreCalculus 1.3 Analyzing the 12 Basic Functions

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Identity
Equation: ƒ(x)=x
Domain: (-∞,∞)
Range: (-∞,∞)
Continuous: Yes
Increasing intervals: (-∞,∞)
Decreasing intervals; N/A
Symmetry: Even
Boundedness: not bounded
Local/Absolute extrema: N/A
Aysmptote: N/A
End Behavior: lim x→ - ∞f(x)=-∞
limx→ ∞f(x)= ∞
Squaring
Equation: ƒ(x)=x²
Domain: (-∞,∞)
Range: [0,∞)
Continuous: Yes
Increasing intervals: (0,∞)
Decreasing intervals: (-∞,0)
Symmetry: Even
Boundedness: below
Local/Absolute extrema: (0,0)
Aysmptote: N/A
End Behavior: lim x→ - ∞f(x)=∞
limx→ ∞f(x)= ∞
Cubing
Equation: ƒ(x)=x³
Domain: [0,∞)
Range: [0,∞)
Continuous: Yes
Increasing intervals: (-∞,∞)
Decreasing intervals; N/A
Symmetry: Even
Boundedness: not bounded
Local/Absolute extrema: N/A
Aysmptote: N/A
End Behavior: lim x→ - ∞f(x)=-∞
limx→ ∞f(x)= ∞
Square Root
Equation: ƒ(x)=√x
Domain: [0,∞)
Range: [0,∞)
Continuous: Yes
Increasing intervals: (0,∞)
Decreasing intervals; N/A
Symmetry: Neither
Boundedness: below
Local/Absolute extrema: minimum: (0,0)
Aysmptote: N/A
End Behavior: lim x→ - ∞f(x)=∞
limx→ ∞f(x)= ∞
Logarithm
Equation: ƒ(x)=ln^x
Domain: (0,∞)
Range: All Real Numbers
Continuous: Yes
Increasing intervals: N/A
Decreasing intervals; N/A
Symmetry: Neither
Boundedness: not bounded
Local/Absolute extrema: N/A
Aysmptote: vertical: x=0
End Behavior: lim x→ - ∞f(x)=∞
limx→ ∞f(x)= ∞
Expotential
Equation: ƒ(x)=e^x
Domain: All Real Numbers
Range: 0,∞)
Continuous: Yes
Increasing intervals: (-∞,∞)
Decreasing intervals; N/A
Symmetry: Neither
Boundedness: below
Local/Absolute extrema: N/A
Aysmptote: horizontal: y=0
End Behavior: lim x→ - ∞f(x)=0
limx→ ∞f(x)= ∞
Reciprocal
Equation: ƒ(x)=1/x
Domain: (-∞,0) U (0,∞)
Range: (-∞,0) U (0,∞)
Continuous: Yes
Increasing intervals: N/A
Decreasing intervals; (-∞,0) (0,∞)
Symmetry: Odd
Boundedness: not bounded
Local/Absolute extrema: N/A
Aysmptote: horizontal: y=0 vertical: x=0
End Behavior: lim x→ - ∞f(x)= ∞
limx→ ∞f(x)= ∞
Sine
Equation: ƒ(x)= sin(x)
Domain: All Real Numbers
Range: [-1,1]
Continuous: Yes
Increasing intervals: Alternatly Increasing/ Decreasing
Decreasing intervals; Alternatly Increasing/ Decreasing
Symmetry: Odd
Boundedness: bounded
Local/Absolute extrema: max: 1 min: -1
Aysmptote: N/A
End Behavior: lim x→ - ∞f(x)= N/A
limx→ ∞f(x)= N/A
Cosine
Equation: ƒ(x)=cos(x)
Domain: All Real Numbers
Range: [0, ∞)
Continuous: Yes
Increasing intervals: Alternatly Increasing/Decreasing
Decreasing intervals; Alternatly Increasing/Decreasing
Symmetry: Even
Boundedness: bounded
Local/Absolute extrema: max: 1 min: -1
Aysmptote: horizontal: N/A
End Behavior: lim x→ - ∞f(x)= N/A
limx→ ∞f(x)= N/A
Greatest Interger
Equation: ƒ(x)=int(x)
Domain: All Real Numbers
Range: all intergers
Continuous: No
Increasing intervals: N/A
Decreasing intervals; N/A
Symmetry: Neither
Boundedness: not bounded
Local/Absolute extrema: N/A
Aysmptote: horizontal: y=0 vertical: x=0
End Behavior: lim x→ - ∞f(x)= -∞
limx→ ∞f(x)= ∞
Absolute Value
Equation: ƒ(x)=abs(x)
Domain: All Real Numbers
Range: [0,∞)
Continuous: Yes
Increasing intervals: (-∞,0)
Decreasing intervals; (0,∞)
Symmetry: Even
Boundedness: Below
Local/Absolute extrema: min: (0,0)
Aysmptote: N/A
End Behavior: lim x→ - ∞f(x)= ∞
limx→ ∞f(x)= ∞
Logistic Function
Equation: ƒ(x)=1/1+e^x
Domain: All Real Numbers
Range: (0,1)
Continuous: Yes
Increasing intervals: (-∞,∞)
Decreasing intervals; N/A
Symmetry: Neither
Boundedness: Bounded
Local/Absolute extrema: N/A
Aysmptote: y=0 & y=1
End Behavior: lim x→ - ∞f(x)= 0
limx→ ∞f(x)= 1