Basic Functions and Graphs Flashcards

Questions and Answers

What is the equation for the Identity Function?

y = 1/x

y = √x

y = x (correct)

y = x^2

What is the range of The Squaring Function?

[0,∞)

The Cubing Function has any discontinuities.

False

Which function has a domain of (-∞,0) ∪ (0,∞)?

The Reciprocal Function Signup and view all the answers

What type of symmetry does The Absolute Value Function have?

Even Signup and view all the answers

What is the range of The Exponential Function?

(0,∞) Signup and view all the answers

The Natural Log Function has a vertical asymptote at x=0.

True Signup and view all the answers

What is the bounded condition of The Sine Function?

Bounded or BOTH @ y=1 & y=-1 Signup and view all the answers

What is the equation for The Logistic Function?

y = 1/(1+e^-x) Signup and view all the answers

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

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.