Podcast
Questions and Answers
What is the equation for the Identity Function?
What is the equation for the Identity Function?
What is the range of The Squaring Function?
What is the range of The Squaring Function?
[0,∞)
The Cubing Function has any discontinuities.
The Cubing Function has any discontinuities.
False
Which function has a domain of (-∞,0) ∪ (0,∞)?
Which function has a domain of (-∞,0) ∪ (0,∞)?
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What type of symmetry does The Absolute Value Function have?
What type of symmetry does The Absolute Value Function have?
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What is the range of The Exponential Function?
What is the range of The Exponential Function?
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The Natural Log Function has a vertical asymptote at x=0.
The Natural Log Function has a vertical asymptote at x=0.
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What is the bounded condition of The Sine Function?
What is the bounded condition of The Sine Function?
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What is the equation for The Logistic Function?
What is the equation for The Logistic Function?
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Study Notes
Identity Function
- Formula: y = x
- Domain: All real numbers
- Range: All real numbers
- No discontinuities; strictly increasing
- Displays odd symmetry around the origin
- Unbounded both above and below
Squaring Function
- Formula: y = x²
- Domain: All real numbers
- Range: [0, ∞)
- Decreasing on the interval (-∞, 0], increasing on [0, ∞)
- Displays even symmetry across the y-axis
- Bounded below at y=0
Cubing Function
- Formula: y = x³
- Domain: All real numbers
- Range: All real numbers
- No discontinuities; strictly increasing
- Displays odd symmetry around the origin
- Unbounded in both directions
Reciprocal Function
- Formula: y = 1/x
- Domain: (-∞, 0) ∪ (0, ∞)
- Range: (-∞, 0) ∪ (0, ∞)
- Discontinuity at x=0 (vertical asymptote)
- Decreasing on (-∞, 0) and increasing on (0, ∞)
- Displays odd symmetry around the origin
- Not bounded
Square Root Function
- Formula: y = √x
- Domain: [0, ∞)
- Range: [0, ∞)
- No discontinuities; strictly increasing
- No symmetry
- Bounded below at y=0
Absolute Value Function
- Formula: y = |x|
- Domain: All real numbers
- Range: [0, ∞)
- Decreasing on (-∞, 0] and increasing on [0, ∞)
- Displays even symmetry across the y-axis
- Bounded below at y=0
Greatest Integer Function
- Formula: y = int(x)
- Domain: All real numbers
- Range: Integer values (ℤ)
- Features multiple jumps (discontinuities)
- Non-decreasing, increasing by integers
- No symmetry
- Unbounded in both directions
Exponential Function
- Formula: y = e^x
- Domain: All real numbers
- Range: (0, ∞)
- No discontinuities; strictly increasing
- No symmetry
- Bounded below at y=0
Natural Logarithm Function
- Formula: y = ln(x)
- Domain: (0, ∞)
- Range: All real numbers
- Discontinuity at x=0 (vertical asymptote)
- Strictly increasing
- No symmetry
- Unbounded in both directions
Sine Function
- Formula: y = sin(x)
- Domain: All real numbers
- Range: [-1, 1]
- Alternates between increasing and decreasing intervals
- Displays odd symmetry around the origin
- Bounded above at y=1 and below at y=-1
Cosine Function
- Formula: y = cos(x)
- Domain: All real numbers
- Range: [-1, 1]
- Alternates between increasing and decreasing intervals
- Displays even symmetry across the y-axis
- Bounded above at y=1 and below at y=-1
Logistic Function
- Formula: y = 1/(1 + e^-x)
- Domain: All real numbers
- Range: (0, 1)
- Discontinuities at y=0 and y=1 (horizontal asymptotes)
- Strictly increasing across its domain
- No symmetry
- Bounded below at y=0 and above at y=1
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Description
This quiz focuses on essential mathematical functions and their graphical representations, including the identity and squaring functions. Each function is accompanied by details about its domain, range, symmetry, and intervals. Perfect for mastering the basics of functions and their characteristics.
