M3 U1 Review: Functions and Key Features

[-2, 3]

[-2, 3)

(-2, 3]

[-3, 4]

(-3, 4]

(-8, 4]

(-8,-3) U [-1, 4]

[-8,-3) U [-1, 4]

(-8,-4] U [-1, 4]

(-2, 6]

$\left(-\infty,\ -3\right]$

$\left[3,\ -\infty\right)$

$\left(-\infty,3\right]$

None of the answer choices

 $\left[-3,\ \infty\right)$  

$\left(-\infty,\ -3\right]$

$\left[3,\ -\infty\right)$

$\left(-\infty,3\right]$

$\left(-\infty,\infty\right)$

None of the answer choices

[-7, 5)

(-3, 1]

[-3, 1)

(-7, 5]

 $\left(-3,\ 0\right)$  

(0, 3)

(-3, 3)

[-4, 5]

 $\left(-\infty,\infty\right)$  

 $\left(-\infty,\ 0\right)\cup\left(0,\ \infty\right)$  

nowhere (no solution)

 $\left(0,\ \infty\right)$  

(∞, 3)

(3, -∞)

(3, ∞)

(-∞, 3)

positive (-2,1) and (3,∞) and negative (-∞,-2) and (1,3)

positive (-∞,-1) and (2,∞) and negative (-1,2)

positive (-1,4) and negative (2,-2)

positive (∞,3) and (1,-2) and negative (3,1) and (-2,-∞)

increasing (-∞,∞) and decreasing nowhere

increasing nowhere and decreasing (-∞,∞)

increasing (1,∞) and decreasing (-∞,1)

increasing (-1,∞) and decreasing (-∞,-1)

positive (1,∞) and negative (-∞,1)

positive (0,∞) and negative (-∞,-1)

positive (-∞,∞) and negative nowhere

positive (∞,1) and negative (1,-∞)

[1, 6]

[120, 200]

[0, 7]

[3, 4]

no maximum

minimum (-4,-1)

no minimum

maximum (-3, 1)

no maximum

minimum (-1,-4)

maximum (-3,1)

minimum (0,-3)

x = -4

x = -2

x = 0

x = 3

Does Not Exist

x = 1

x = 3

x = 4

x = 5

Does Not Exist

x = 8

x = 4

$\infty$

x = 2

Local max at x = -3

Local min at x = -3

Local max at x = 1

Local min at x = -3

Local max at x = -3

Local min at x = 1

$\left(-\infty,\ \infty\right)$

[13,14]

[13, 17]

[16, 17]

[16, 19]

-1

1

1/2

2

5

-1/5

-5

15