Key Features Review

Key Features of Functions

REVIEW

Domain & Range

• Domain = x-values = input

• Range = y-values = output

Multiple Choice

What is the domain of the graph?

• y≥1
• x ≥ 1
• All real numbers
• none of these

Multiple Choice

What is the range of the graph?

• y≥1
• x≥1
• All real numbers
• none of these

Multiple Choice

What is the DOMAIN?

• (4, ∞)
• (-4, ∞)
• [-3, 3)
• (-3, 3]

Multiple Choice

What is the RANGE?

• {-3, 3]
• all real numbers
• [-4, 5]
• [-4, ∞)

Intervals of Increase & Decrease

• Domain intervals = use x-values

• Increasing = positive rate of change

• Decreasing = negative rate of change

Multiple Choice

When is this function increasing?

• (-3, 3)

• (-2.5, 2.5)

• [-3, 3]

• (3, ∞)

Multiple Choice

Where is the function decreasing?

• (-∞, -1)
• (-1, ∞)
• (-∞, 3)
• (-∞, ∞)

Multiple Choice

When is the function decreasing?

• (30, 55)

• (40, 60]

• (15, 40)

• (60, -40)

Maximums & Minimums

• Maximum = high points

• Minimum = low points

• Relative/local = highest or lowest point for the area

• Absolute = highest or lowest for the function

Multiple Choice

What is the absolute max?

• (0, 36)
• (−2.55, −6.55), (2.55, −6.55)
• (−∞, ∞)
• None

Multiple Choice

What are the local maxima of this graph?

• local maximum at (2.2, 3.9)
• local maximum at (-8, 5)
• local maximum at (5, -8)⋃(3.9, 2.2)
• local maximum at (-8, 5)⋃(2.2, 3.9)

Multiple Choice

Which coordinate point describes the location of the minimum point of this function?

• (-2, -1)

• (0, -1)

• (-1, -2)

• (-5, 3)

Multiple Choice

Does this graph have a minimum or maximum? What point?

• Minimum at (0, 0)

• Minimum at (0, 2)

• Maximum at (0, 0)

• Maximum at (0, 2)

Multiple Choice

Does this graph have a minimum or maximum? What point?

• minimum at (-3, -5)

• minimum at (3, 5)

• maximum at (-3, -5)

• maximum at (3, 5)

Multiple Choice

Which of the following does this graph not show?

• absolute max
• absolute min
• relative max
• relative min

Intercepts

• x-intercepts are where the function crosses the x-axis, when y equals zero

• y-intercepts are where the function crosses the y-axis, when x equals zero

Multiple Choice

What is the x and y intercept for the following equation ?
4x - 10y = 20

• x - int = 4    
  y-int = -10
• x-int = 5
  y-int = 2
• x - int = 5
  y int = -2
• x -int = 4
  y -int = -10

Multiple Choice

What are all the y-intercepts?

• (0, -6.25)
• (-3,0), (-2,0), (2,0), (3,0)
• (0, 36)
• (-∞, ∞)

Multiple Choice

What are all the x-intercepts?

• (-2.55, 0), (2.55, 0)
• (-3,0), (-2,0), (2,0), (3,0)
• (0, 36)
• (-∞,∞)