ALL Functions

Question 1

Linear Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations
Example

Answer 1

Parent Function: f(x) = x
Graph Shape: Straight line
Domain: All real numbers
Range: All real numbers
End Behavior: Left ↓, Right ↑ (if m > 0)
Special Properties: Constant Rate of Change (slope)
Transformations: m = slope change, b = vertical shift

Question 2

Quadratic Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations
Example

Answer 2

Parent Function: f(x) = x²
Graph Shape: Parabola (U-shaped)
Domain: All Reals
Range: [Minimum, Infinity) OR (Infinity, Maximum]
End Behavior: Both ends ↑ (if a > 0) or ↓ (if a < 0)
Special Properties: Vertex, Axis of Symmetry
Transformations: a = stretch/flip, h = horizontal shift, k = vertical shift
Ex: y= a (x - h)² + k

Question 3

Square Root Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations
Example

Answer 3

Parent Function: f(x) = √x
Graph Shape: Curve starting at a point, increasing slowly
Domain: [h, infinity)
Range: [k, infinity)
End Behavior: Increases but levels off
Special Properties: Starts at (h, k), no negatives under radical
Transformations: a = stretch/flip, h = shift L/R, k = shift U/D
Ex: y = a√(x - h) + k

Question 4

Cube Root Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations
Example

Answer 4

Parent Function: f(x) = ³√x
Graph Shape: S-shaped curve
Domain: All Reals
Range: All Real
End Behavior: Left ↓, Right ↑
Special Properties: Passes through inflection point
Transformations: a = stretch/flip, h = horizontal shift, k = vertical shift
y = a³√(x - h) + k

Question 5

Exponential Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations
Example

Answer 5

Parent Function: f(x) = bˣ
Graph Shape: Growth (J Shape) or Decay (Flipped J)
Domain: All Reals
Range:
- If a > 0, (HA, ꝏ)
- If a < 0, (-ꝏ, HA)
End Behavior: Approaches HA & Grows/Decays on different sides
Special Properties: Horizontal Asymptote
Transformations: a = vertical stretch/flip, b = growth factor, k = vertical shift
Ex: y = a (b)ˣ⁻ʰ + k

Question 6

Logarithmic Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations
Example

Answer 6

Parent Function: f(x) = log (x)
Graph Shape: Curve following VA
Domain: (VA, Infinity)
Range: All Reals
End Behavior: Approaches VA & Other Grows
Special Properties: Inverse of Exponential Functions
Transformations: a = stretch/flip, h = horizontal shift, k = vertical shift
Ex: y = a · log(x - h) + k

Question 7

Rational Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations

Answer 7

Parent Function: f(x) = 1/x
Graph Shape: Two Hyperbola Branches
Domain: All Reals, Restriction = VA & Hole in Function
Range: Use Calc (Depends on Variations)
End Behavior: Approaches Asymptotes
Special Properties: VA, HA, holes possible
Transformations: a = stretch/flip, h = horizontal shift, k = vertical shift

Question 8

Sine Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations

Question 9

Cosine Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations

Question 10

Tangent Functions

List all of the following properties:
Parent Function
Graph Shape
Domain
Range
End Behavior
Special Properties
Transformations