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Function Characteristics part 2
Describe characteristics of functions involving the behavior of the graph.
20
Mathematics
11th Grade
12/13/2011

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Term

 

[image]

 

Definition

Intervals of increase: (1, 3]

 

Intervals of decrease: [-1, 1]

 

Rate of change: -1 and 1

 

Axis of symmetry: x = 1

 

Asymptotes : none


 

Term
[image]
Definition

 

Intervals of increase: (-2, ∞)

 

Intervals of decrease: [-∞, -2]

 

Rate of change: quadratic

 

Axis of symmetry: x = -2

 

Asymptotes : none

 

 

 
Term
[image]
Definition

 

Intervals of increase: [-1, 2]

 

Intervals of decrease: none

 

Rate of change: 1

 

Axis of symmetry: y = -x + 1

 

Asymptotes : none

 

 

 
Term
[image]
Definition

 

Intervals of increase: (0, ∞)

 

Intervals of decrease: (-∞, 0]

 

Rate of change: -1 and 1

 

Axis of symmetry: x = 0

 

Asymptotes : none

 

 

 
Term
[image]
Definition

 

Intervals of increase: [1, 11]

 

Intervals of decrease: none

 

Rate of change: 5

 

Axis of symmetry: none

 

Asymptotes : none

 

 

 
Term

Assume height is input and shoe size is output

[image]

Definition

 

Intervals of increase: [53, 58], (62, 67], (70, 74]

 

Intervals of decrease: (58, 62], (67, 70]

 

Rate of change: variable

 

Axis of symmetry: none

 

Asymptotes : none

 

 

 

Term
[image]
Definition

 

Intervals of increase: (-∞, ∞)

 

Intervals of decrease: none

 

Rate of change: variable

 

Axis of symmetry: none

 

Asymptotes : none

 

 

 
Term
[image]
Definition

Intervals of increase: (-∞, ∞)

 

Intervals of decrease: none

 

Rate of change: variable

 

Axis of symmetry: none

 

Asymptotes : none

 
Term

X

Y

0

1

–1

–2

–2

–3

–3

–2

–4

1

Definition

Intervals of increase: (-2, 0]

 

Intervals of decrease: (-4, -2]

 

Rate of change: quadratic

 

Axis of symmetry: x = -2

 

Asymptotes : none

 
Term
[image]
Definition

Intervals of increase: (-∞, 1]

 

Intervals of decrease: (1, ∞)

 

Rate of change: quadratic

 

Axis of symmetry: x = 1

 

Asymptotes : none

 
Term
[image]
Definition

Intervals of increase: approximately (-∞, -1.8] and (1.8, ∞)

 

Intervals of decrease: approximately (-1.8, 1.8)

 

Rate of change: variable

 

Axis of symmetry: none

 

Asymptotes : none

 
Term
[image]
Definition

Intervals of increase: none

 

Intervals of decrease: (-∞, 1) and (1, ∞)

 

Rate of change: variable

 

Axis of symmetry: y = -x + 2

 

Asymptotes : x = 1 and y = 1

 

 

Term
[image]
Definition

Intervals of increase: (2, 3]

 

Intervals of decrease: [1, 2)none

 

Rate of change: -1 and 1

 

Axis of symmetry: x = 2

 

Asymptotes : none

 
Term
[image]
Definition

 Intervals of increase: none

 

Intervals of decrease: (-∞, ∞)

 

Rate of change: variable

 

Axis of symmetry: none

 

Asymptotes : y = 0

 

 

Term
[image]
Definition

Intervals of increase: (0, ∞)

 

Intervals of decrease: (-∞, 0]

 

Rate of change: - 1 and variable

 

Axis of symmetry: none

 

Asymptotes : none

 
Term
f(x) = x2
Definition

Intervals of increase: (0, ∞)

 

Intervals of decrease: (-∞, 0]

 

Rate of change: quadratic

 

Axis of symmetry: x = 0

 

Asymptotes : none

 
Term

 

[image]

Definition

Intervals of increase: none

 

Intervals of decrease: (-∞, 3]

 

Rate of change: variable

 

Axis of symmetry: none

 

Asymptotes : none

Term
y = -4x + 3
Definition

Intervals of increase: none

 

Intervals of decrease: (-∞, ∞)

 

Rate of change: -4

 

Axis of symmetry: ∞ many

 

Asymptotes : none

Term

y =      1    

           x + 4

Definition

Intervals of increase: none

 

Intervals of decrease: (-∞, -4) and (-4, ∞)

 

Rate of change: variable

 

Axis of symmetry: y = -x - 4 

 

Asymptotes : x = -4 and y = 0

Term
g(x) = ιx - 1ι + 3 
Definition

Intervals of increase: (1, ∞)

 

Intervals of decrease: (-∞, 1]

 

Rate of change: -1 an 1

 

Axis of symmetry: x = 1

 

Asymptotes : none

 

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