basic functions review
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Last updated 2:09 PM on 8/30/23
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8 Terms
1
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The Identity Function
y\=x
y\=x
Domain: ALL REALS
Range: ALL REALS
Discontinuities: None
Decreasing Intervals: None
Increasing Intervals: (-∞,∞)
Symmetry: ODD (about the origin)
Bounded: Unbounded or NONE
Range: ALL REALS
Discontinuities: None
Decreasing Intervals: None
Increasing Intervals: (-∞,∞)
Symmetry: ODD (about the origin)
Bounded: Unbounded or NONE
2
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The Squaring Function
y \= x^2
y \= x^2
Domain: ALL REALS
Range: [0,∞)
Discontinuities: None
Decreasing Intervals: (-∞,0]
Increasing Intervals: [0,∞)
Symmetry: EVEN (across y-axis)
Bounded: Bounded Below
Range: [0,∞)
Discontinuities: None
Decreasing Intervals: (-∞,0]
Increasing Intervals: [0,∞)
Symmetry: EVEN (across y-axis)
Bounded: Bounded Below
3
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The Cubing Function
y\=x^3
y\=x^3
Domain: ALL REALS
Range: ALL REALS
Discontinuities: NONE
Decreasing Intervals: NONE
Increasing Intervals: All REALS
Symmetry: ODD (about the origin)
Bounded: Unbounded or NONE
Range: ALL REALS
Discontinuities: NONE
Decreasing Intervals: NONE
Increasing Intervals: All REALS
Symmetry: ODD (about the origin)
Bounded: Unbounded or NONE
4
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The Reciprocal Function
y\=1/x
y\=1/x
Domain: (-∞,0) ∪ (0,∞)
Range: (-∞,0) ∪ (0,∞)
Discontinuities: NONE **Asymp @ x\=0 (VA)**
Decreasing Intervals: (-∞,0)
Increasing Intervals: (0, ∞)
Symmetry: ODD (about the origin)
Bounded: Not Bounded or NONE
Range: (-∞,0) ∪ (0,∞)
Discontinuities: NONE **Asymp @ x\=0 (VA)**
Decreasing Intervals: (-∞,0)
Increasing Intervals: (0, ∞)
Symmetry: ODD (about the origin)
Bounded: Not Bounded or NONE
5
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The Square Root Function
y\=√x
y\=√x
Domain: [0,∞)
Range: [0,∞)
Discontinuities: NONE
Decreasing Intervals: NONE
Increasing Intervals: [0, ∞)
Symmetry: NONE
Bounded: Bounded Below
Range: [0,∞)
Discontinuities: NONE
Decreasing Intervals: NONE
Increasing Intervals: [0, ∞)
Symmetry: NONE
Bounded: Bounded Below
6
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The Absolute Value Function
y\=|x|
y\=|x|
Domain: ALL REALS
Range: [0,∞)
Discontinuities: NONE
Decreasing Intervals: (-∞, 0]
Increasing Intervals: [0, ∞)
Symmetry: EVEN (across the y-axis)
Bounded: Bounded Below
Range: [0,∞)
Discontinuities: NONE
Decreasing Intervals: (-∞, 0]
Increasing Intervals: [0, ∞)
Symmetry: EVEN (across the y-axis)
Bounded: Bounded Below
7
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The Greatest Integer Function
y\=int(x)
y\=int(x)
Domain: ALL REALS
Range: Integers or "Z"
Discontinuities: Multiple Jumps
Decreasing Intervals: NONE
Increasing Intervals: By Integers
Symmetry: NONE
Bounded: Unbounded or NONE
Range: Integers or "Z"
Discontinuities: Multiple Jumps
Decreasing Intervals: NONE
Increasing Intervals: By Integers
Symmetry: NONE
Bounded: Unbounded or NONE
8
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The Exponential Function
y\=e^x
y\=e^x
Domain: ALL REALS
Range: (0,∞)
Discontinuities: NONE
Decreasing Intervals: NONE
Increasing Intervals: (-∞,∞)
Symmetry: NONE
Bounded: Bounded Below
Range: (0,∞)
Discontinuities: NONE
Decreasing Intervals: NONE
Increasing Intervals: (-∞,∞)
Symmetry: NONE
Bounded: Bounded Below