12 Basic Functions w/ Graphs

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12 Terms

1
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The Identity Function

y=x

Domain: ALL REALS

Range: ALL REALS

Discontinuities: None

Decreasing Intervals: None

Increasing Intervals: (-∞,∞)

Symmetry: ODD (about the origin)

Bounded: Unbounded or NONE

<p>Domain: ALL REALS</p><p>Range: ALL REALS</p><p>Discontinuities: None</p><p>Decreasing Intervals: None</p><p>Increasing Intervals: (-∞,∞)</p><p>Symmetry: ODD (about the origin)</p><p>Bounded: Unbounded or NONE</p>
2
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The Squaring Function

y = x^2

Domain: ALL REALS

Range: [0,∞)

Discontinuities: None

Decreasing Intervals: (-∞,0]

Increasing Intervals: [0,∞)

Symmetry: EVEN (across y-axis)

Bounded: Bounded Below

<p>Domain: ALL REALS</p><p>Range: [0,∞)</p><p>Discontinuities: None</p><p>Decreasing Intervals: (-∞,0]</p><p>Increasing Intervals: [0,∞)</p><p>Symmetry: EVEN (across y-axis)</p><p>Bounded: Bounded Below</p>
3
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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

<p>Domain: ALL REALS</p><p>Range: ALL REALS</p><p>Discontinuities: NONE</p><p>Decreasing Intervals: NONE</p><p>Increasing Intervals: All REALS</p><p>Symmetry: ODD (about the origin)</p><p>Bounded: Unbounded or NONE</p>
4
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The Reciprocal Function

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

<p>Domain: (-∞,0) ∪ (0,∞)</p><p>Range: (-∞,0) ∪ (0,∞)</p><p>Discontinuities: NONE **Asymp @ x=0 (VA)**</p><p>Decreasing Intervals: (-∞,0)</p><p>Increasing Intervals: (0, ∞)</p><p>Symmetry: ODD (about the origin)</p><p>Bounded: Not Bounded or NONE</p>
5
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The Square Root Function

y=√x

Domain: [0,∞)

Range: [0,∞)

Discontinuities: NONE

Decreasing Intervals: NONE

Increasing Intervals: [0, ∞)

Symmetry: NONE

Bounded: Bounded Below

<p>Domain: [0,∞)</p><p>Range: [0,∞)</p><p>Discontinuities: NONE</p><p>Decreasing Intervals: NONE</p><p>Increasing Intervals: [0, ∞)</p><p>Symmetry: NONE</p><p>Bounded: Bounded Below</p>
6
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The Absolute Value Function

y=|x|

Domain: ALL REALS

Range: [0,∞)

Discontinuities: NONE

Decreasing Intervals: (-∞, 0]

Increasing Intervals: [0, ∞)

Symmetry: EVEN (across the y-axis)

Bounded: Bounded Below

<p>Domain: ALL REALS</p><p>Range: [0,∞)</p><p>Discontinuities: NONE</p><p>Decreasing Intervals: (-∞, 0]</p><p>Increasing Intervals: [0, ∞)</p><p>Symmetry: EVEN (across the y-axis)</p><p>Bounded: Bounded Below</p>
7
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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

<p>Domain: ALL REALS</p><p>Range: Integers or "Z"</p><p>Discontinuities: Multiple Jumps</p><p>Decreasing Intervals: NONE</p><p>Increasing Intervals: By Integers</p><p>Symmetry: NONE</p><p>Bounded: Unbounded or NONE</p>
8
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The Exponential Function

y=e^x

Domain: ALL REALS

Range: (0,∞)

Discontinuities: NONE

Decreasing Intervals: NONE

Increasing Intervals: (-∞,∞)

Symmetry: NONE

Bounded: Bounded Below

<p>Domain: ALL REALS</p><p>Range: (0,∞)</p><p>Discontinuities: NONE</p><p>Decreasing Intervals: NONE</p><p>Increasing Intervals: (-∞,∞)</p><p>Symmetry: NONE</p><p>Bounded: Bounded Below</p>
9
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The Natural Log Function

y=ln(x)

Domain: (0,∞)

Range: ALL REALS

Discontinuities: NONE **Asymp @ x=0 (VA)**

Decreasing Intervals: NONE

Increasing Intervals: (-∞,∞)

Symmetry: NONE

Bounded: Unbounded or NONE

<p>Domain: (0,∞)</p><p>Range: ALL REALS</p><p>Discontinuities: NONE **Asymp @ x=0 (VA)**</p><p>Decreasing Intervals: NONE</p><p>Increasing Intervals: (-∞,∞)</p><p>Symmetry: NONE</p><p>Bounded: Unbounded or NONE</p>
10
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The Sine Function

y=sin(x)

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

<p>Domain: ALL REALS</p><p>Range: [-1,1]</p><p>Discontinuities: NONE</p><p>Decreasing Intervals: It Alternates</p><p>Increasing Intervals: It Alternates</p><p>Symmetry: ODD (about the origin)</p><p>Bounded: Bounded or BOTH @ y=1 &amp; y=-1</p>
11
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The Cosine Function

y=cos(x)

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

<p>Domain: ALL REALS</p><p>Range: [-1,1]</p><p>Discontinuities: NONE</p><p>Decreasing Intervals: It Alternates</p><p>Increasing Intervals: It Alternates</p><p>Symmetry: EVEN (across the y-axis)</p><p>Bounded: Bounded or BOTH @ y=1 &amp; y=-1</p>
12
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The Logistic Function

y=1/1+e^-x

feel free to change scale of graph

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

<p>Domain: ALL REALS</p><p>Range: (0,1)</p><p>Discontinuities: NONE **Asymp @ y=0 &amp; y=1 (HA)**</p><p>Decreasing Intervals: NONE</p><p>Increasing Intervals: ALL REALS</p><p>Symmetry: NONE</p><p>Bounded: Bounded or BOTH @ y=0 &amp; y=1</p>