12 Basic Functions w/ Graphs – Flashcards
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The Identity Function
y=x
answer
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
answer
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
answer
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
answer
Domain: (-β,0) βͺ (0,β)
Range: (-β,0) βͺ (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=βx
answer
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|
answer
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)
answer
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
answer
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)
answer
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)
answer
Domain: ALL REALS
Range: [-1,1]
Discontinuities: NONE
Decreasing Intervals: It Alternates
Increasing Intervals: It Alternates
Symmetry: ODD (about the origin)
Bounded: Bounded or BOTH @ y=1 & y=-1
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The Cosine Function
y=cos(x)
answer
Domain: ALL REALS
Range: [-1,1]
Discontinuities: NONE
Decreasing Intervals: It Alternates
Increasing Intervals: It Alternates
Symmetry: EVEN (across the y-axis)
Bounded: Bounded or BOTH @ y=1 & y=-1
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The Logistic Function
y=1/1+e^-x
*feel free to change scale of graph*
answer
Domain: ALL REALS
Range: (0,1)
Discontinuities: NONE **Asymp @ y=0 & y=1 (HA)**
Decreasing Intervals: NONE
Increasing Intervals: ALL REALS
Symmetry: NONE
Bounded: Bounded or BOTH @ y=0 & y=1
