Lesson 1-4: Analyzing Functions

Increasing: (-∞,-3)∪(1,∞)

Decreasing: (-3,1)

Name the domain interval(s) where the function is increasing and decreasing.

Relative Maximum: (-3,-1)

Relative Minimum: (1,-4)

Classify the function's extrema (Relative / Absolute, Maximum / Minimum), and name their coordinates @ (x, y)

Increasing: (-2,-1)∪(-1,0)

Decreasing: (-∞,-2)∪(0,∞)

Name the domain interval(s) where the function is increasing and decreasing.

Relative Minimum @ (-2,2)

Relative Maximum @ (0,0)

Classify the function's extrema (Relative or Absolute, Maximum or Minimum), and name their coordinates @ (x, y)

Domain: (-∞,-1)∪(-1,∞)

Range: (-∞,0]∪[2,∞)

State the Domain and Range of the function shown.

As x→∞, f(x)→∞

As x→-∞, f(x)→-∞

Describe the end behavior of the function shown.

Infinite Discontinuity @ x=-1

Describe the continuity of the function shown.

Increasing: (-4,4)

Decreasing: (-∞,-4)∪(4,∞)

Name the domain interval(s) where the function is increasing and decreasing.

Relative Maximum @ (4, 2)

Relative Minimum @ (-4,-2)

Classify the function's extrema (Relative or Absolute, Maximum or Minimum), and name their coordinates @ (x, y)

Domain: (-∞,∞)

Range: [-2,2]

State the Domain and Range of the function shown.

As x→∞, f(x)→0

As x→-∞, f(x)→0

Describe the end behavior of the function shown.

Continuous for entire domain

(-∞,∞)

Describe the continuity of the function shown.

Increasing: (-1,0)∪(1,∞)

Decreasing: (-∞,-1)∪(0,1)

Name the domain interval(s) where the function is increasing and decreasing.

Relative Minimums

@ (-1,-1) and (1,-1)

Relative Maximum

@ (0,0)

Classify the function's extrema (Relative or Absolute, Maximum or Minimum), and name their coordinates @ (x, y)

Domain: (-∞,∞)

Range: [-1,∞)

State the Domain and Range of the function shown.

As x→∞, f(x)→∞

As x→-∞, f(x)→∞

Describe the end behavior of the function shown.

Continuous for entire domain

(-∞,∞)

Describe the continuity of the function shown.

Increasing: (-∞,3)

Decreasing: (3,∞)

Name the domain interval(s) where the function is increasing and decreasing.

Absolute Maximum @ (3,5)

Classify the function's extrema (Relative or Absolute, Maximum or Minimum), and name their coordinates @ (x, y)

Domain: (-∞,∞)

Range: (-∞,5]

State the Domain and Range of the function shown.

As x→∞, f(x)→-∞

As x→-∞, f(x)→-∞

Describe the end behavior of the function shown.

Continuous for all domain values

(-∞,∞)

Describe the continuity of the function shown.

Increasing: (-∞,0)∪(2,∞)

Decreasing: (0,2)

Name the domain interval(s) where the function is increasing and decreasing.

Relative Maximum @ (0,-3)

Relative Minimum @ (2,-7)

Classify the function's extrema (Relative or Absolute, Maximum or Minimum), and name their coordinates @ (x, y)

Domain: (-∞,∞)

Range: (-∞,∞)

State the Domain and Range of the function shown.

As x→∞, f(x)→∞

As x→-∞, f(x)→-∞

Describe the end behavior of the function shown.

Continuous for all domain values

(-∞,∞)

Describe the continuity of the function shown.