12 Basic Functions w/ Graphs

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

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

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

The Exponential Function y=e^x

Domain: ALL REALS Range: (0,∞) Discontinuities: NONE Decreasing Intervals: NONE Increasing Intervals: (-∞,∞) Symmetry: NONE Bounded: Bounded Below

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

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

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

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

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

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

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

The Square Root Function y=√x

Domain: [0,∞) Range: [0,∞) Discontinuities: NONE Decreasing Intervals: NONE Increasing Intervals: [0, ∞) Symmetry: NONE Bounded: Bounded Below