Basic Functions Characteristics Quiz

Study Notes

Identity (Linear) Function

Domain: All real numbers (-∞, ∞)
Range: All real numbers (-∞, ∞)
Continuous with no breaks
Always increasing across its domain
Symmetric with respect to the origin (odd symmetry)
Unbounded in both directions
No local extrema present
No horizontal or vertical asymptotes

Squaring (Quadratic) Function

Domain: All real numbers (-∞, ∞)
Range: Non-negative real numbers [0, ∞)
Continuous and unbroken
Decreases on (-∞, 0) and increases on (0, ∞)
Symmetric about the y-axis (even symmetry)
Bounded below by 0
Local minimum at (0, 0) with no maximum
No horizontal or vertical asymptotes

Cubing Function

Domain: All real numbers (-∞, ∞)
Range: All real numbers (-∞, ∞)
Continuous with no interruptions
Always increasing throughout the entire domain
Exhibits odd symmetry
Unbounded in both directions
No local extrema present
No horizontal or vertical asymptotes

Square Root Function

Domain: Non-negative real numbers [0, ∞)
Range: Non-negative real numbers [0, ∞)
Continuous and without breaks
Increasing from (0, ∞)
No symmetry
Bounded below by 0
Local minimum at (0, 0) with no maximum
No horizontal or vertical asymptotes

Natural Logarithm Function

Domain: Positive real numbers (0, ∞)
Range: All real numbers (-∞, ∞)
Continuous function
Increasing on (0, ∞)
No symmetry
Unbounded in both directions
No local extrema present
No horizontal asymptotes; vertical asymptote at x=0

Reciprocal Function

Domain: All real numbers except zero (-∞, 0) ∪ (0, ∞)
Range: All real numbers except zero (-∞, 0)
Contains infinite discontinuities at x=0
Decreasing from (-∞, 0) and from (0, ∞)
Symmetric with respect to the origin (odd symmetry)
Unbounded in both directions
No local extrema
Horizontal asymptote at y=0; vertical asymptote at x=0

Exponential Function

Domain: All real numbers (-∞, ∞)
Range: Positive real numbers (0, ∞)
Continuous function without interruptions
Always increasing over its entire domain
Lacks symmetry
Bounded below by 0
No local extrema present
Horizontal asymptote at y=0

Sine Function

Domain: All real numbers (-∞, ∞)
Range: Values between -1 and 1 inclusive [-1, 1]
Continuous, exhibiting periodic behavior
Alternates between increasing and decreasing in φ (periodic waves)
Symmetric with respect to the origin (odd symmetry)
Bounded within the interval [-1, 1]
Local maximum at (φ, 1) and minimum at (φ, -1)
No horizontal or vertical asymptotes

Cosine Function

Domain: All real numbers (-∞, ∞)
Range: Values between -1 and 1 inclusive [-1, 1]
Continuous with periodic behavior
Alternates between increasing and decreasing in φ (periodic waves)
Symmetric about the y-axis (even symmetry)
Bounded within the interval [-1, 1]
Local maximum at (φ, 1) and minimum at (φ, -1)
No horizontal or vertical asymptotes

Greatest Integer Function

Domain: All real numbers (-∞, ∞)
Range: All integers
Exhibits jump discontinuities
Always increases (pieces) across its domain
No symmetry present
Unbounded in both directions
No local extrema
No horizontal or vertical asymptotes

Absolute Value Function

Domain: All real numbers (-∞, ∞)
Range: Non-negative real numbers [0, ∞)
Continuous with no breaks
Decreases on (-∞, 0) and increases on (0, ∞)
Symmetric about the y-axis (even symmetry)
Bounded below by 0
Local minimum at (0, 0) with no maximum
No horizontal or vertical asymptotes

Logistic Function

Domain: All real numbers (-∞, ∞)
Range: Values between 0 and 1 (0, 1)
Continuous function
Always increasing across its domain
No symmetry present
Bounded within the interval (0, 1)
No local extrema
Horizontal asymptotes at y=0 and y=1

Description

Test your knowledge of the characteristics of basic functions with this quiz. Each flashcard presents a different function, including its domain, range, continuity, and more. Perfect for students looking to strengthen their understanding of function types and their properties.