# 12 Basic Functions w/ Graphs – Flashcards

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The Identity Function y=x
Domain: ALL REALS Range: ALL REALS Discontinuities: None Decreasing Intervals: None Increasing Intervals: (-β,β) Symmetry: ODD (about the origin) Bounded: Unbounded or NONE
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The Squaring Function y = x^2
Domain: ALL REALS Range: [0,β) Discontinuities: None Decreasing Intervals: (-β,0] Increasing Intervals: [0,β) Symmetry: EVEN (across y-axis) Bounded: Bounded Below
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The Cubing Function 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
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The Reciprocal Function y=1/x
Domain: (-β,0) βͺ (0,β) Range: (-β,0) βͺ (0,β) Discontinuities: NONE **Asymp @ x=0 (VA)** Decreasing Intervals: (-β,0) Increasing Intervals: (0, β) Symmetry: ODD (about the origin) Bounded: Not Bounded or NONE
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The Square Root Function y=βx
Domain: [0,β) Range: [0,β) Discontinuities: NONE Decreasing Intervals: NONE Increasing Intervals: [0, β) Symmetry: NONE Bounded: Bounded Below
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The Absolute Value Function y=|x|
Domain: ALL REALS Range: [0,β) Discontinuities: NONE Decreasing Intervals: (-β, 0] Increasing Intervals: [0, β) Symmetry: EVEN (across the y-axis) Bounded: Bounded Below
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The Greatest Integer Function 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
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The Exponential Function y=e^x
Domain: ALL REALS Range: (0,β) Discontinuities: NONE Decreasing Intervals: NONE Increasing Intervals: (-β,β) Symmetry: NONE Bounded: Bounded Below
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The Natural Log Function y=ln(x)
Domain: (0,β) Range: ALL REALS Discontinuities: NONE **Asymp @ x=0 (VA)** Decreasing Intervals: NONE Increasing Intervals: (-β,β) Symmetry: NONE Bounded: Unbounded or NONE
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The Sine Function y=sin(x)