The 12 Basic Functions By Haley Chandler and Sarah Engell

The Identity Function Domain: (-∞, ∞) Range: (-∞, ∞) Increases from (-∞, ∞) Odd because it has rotational symmetry No asymptotes, continuous Real life application:

The Squaring Function Domain: (- ∞, ∞ ) Range: [0, ∞ ) Increases from [0, ∞ ), decreases from (- ∞, 0] Even because it has y-axis symmetry No asymptotes, continuous Real life application:

The Cubing Function Domain: (-∞, ∞) Range: (-∞, ∞) Increases from (-∞, ∞) Odd because it has rotational symmetry No asymptotes, continuous Real life application:

The Reciprocal Function Domain: (-∞, 0) U (0, ∞) Range: (-∞, 0) U (0, ∞) Decreases from (-∞, 0) U (0, ∞) Odd because it has rotational symmetry Horizontal and vertical asymptote of 0 Continuous Real life application: An example of a reciprocal function in real life is the cables on a bridge, they are shaped like a hyperbola because of how they are constructed.

The Square Root Function Domain: [0, ∞) Range: [0, ∞) Increases from [0, ∞) Neither because it does not have any symmetry No asymptotes Continuous [0, ∞) Real life application:

The Exponential Function Domain: (-∞, ∞) Range: (0, ∞) Increases from (-∞, ∞) Neither because it has no symmetry Horizontal asymptote of 0 Continuous Real life application:

The Natural Logarithm Function Domain: (0, ∞) Range: (-∞, ∞) Increases from (0, ∞) Neither because it has no symmetry Vertical asymptote of 0 Continuous Real life application:

The Sine Function Domain: (-∞, ∞) Range: [1,-1] Increases from [-1.5,1.5] Decreases from [1.5,4.5] Odd because it has rotational symmetry No asymptotes, continuous Real life application:

The Cosine Function Domain: (-∞, ∞) Range: [1,-1] Increases from [-3,1] Decreases from [1,3] Even because it has y-axis symmetry No asymptotes, continuous Real life application:

The Absolute Value Function Domain: (-∞, ∞) Range: [0, ∞) Increases from [0, ∞) Decreases from (-∞, 0] Even because it has y-axis symmetry No asymptotes, continuous Real life application:

The Greatest Integer Function Domain and Range: All real numbers Constant at specified intervals Neither because it has no symmetry No asymptotes, not continuous Real life application:

The Logistic Function Domain:(-∞,∞) Range: (0,1) Increases (-∞,∞) No decrease Neither because it has no symmetry Asymptotes: Horizontal 0 and 1 Continuous Real life application