M3 U1 Review: Functions and Key Features

M3 U1 Review: Functions and Key Features

Behaviors and Intervals

Multiple Choice

Look at the Graph. Write the inequality in interval notation.

• [-4, -1)
• (-4, -1)
• (-4, -1]
• [-4, -1]

Multiple Choice

Write the following in interval notation
x ≥ 100

• (0, 100]  (Real quick)
• (∞, 100]
• [100, ∞)
• (∞, 100)

Multiple Choice

Look at the graph. Write the inequality in interval notation.

• (-2,5)
• (-∞,-2)⋃(5,∞)
• [-2,5]
• (-∞,-2]∪[5,∞)

Multiple Choice

Express the following in Interval Notation
-9 < x ≤ -4

• [-9, -4]
• (-9,-4]
• [-9, -4]
• (-9,-4)

Multiple Choice

Express the following in Interval Notation
-8 ≤ x < 8

• [-8, 8]
• [-8,8)
• (-8, 8]
• (-8, 8)

Multiple Choice

What is the range of the graph?

• (-∞,∞)
• [-1,0]
• [-1,3]
• [3,∞)

Multiple Choice

What is the domain?

• [-2, 3]

• [-2, 3)

• (-2, 3]

• [-3, 4]

• (-3, 4]

Multiple Choice

What is the domain?

• (-8, 4]

• (-8,-3) U [-1, 4]

• [-8,-3) U [-1, 4]

• (-8,-4] U [-1, 4]

• (-2, 6]

Multiple Choice

What is the range?

• $\left(-\infty,\ -3\right]$
  

• $\left[3,\ -\infty\right)$
  

• $\left(-\infty,3\right]$

• None of the answer choices

•  $\left[-3,\ \infty\right)$  

Multiple Choice

What is the domain?

• $\left(-\infty,\ -3\right]$
  

• $\left[3,\ -\infty\right)$
  

• $\left(-\infty,3\right]$

• $\left(-\infty,\infty\right)$

• None of the answer choices

Multiple Choice

What is the range of the graph?

• [-7, 5)

• (-3, 1]

• [-3, 1)

• (-7, 5]

Multiple Choice

On what interval (set of x-values) is the function increasing?

•  $\left(-3,\ 0\right)$  
  

• (0, 3)

• (-3, 3)

• [-4, 5]

Multiple Choice

For what interval (values of x) is this function

 $f\left(x\right)>0$  ?

•  $\left(-\infty,\infty\right)$  
  

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

• nowhere (no solution)

•  $\left(0,\ \infty\right)$  

Multiple Choice

On what interval is the graph decreasing?

• (∞, 3)

• (3, -∞)

• (3, ∞)

• (-∞, 3)

Multiple Choice

Where is the function positive and where is it negative?

• 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,-∞)

Multiple Choice

Where is the function increasing and decreasing?

• increasing (-∞,∞) and decreasing nowhere

• increasing nowhere and decreasing (-∞,∞)

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

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

Multiple Choice

Where is the function positive and where is it negative?

• positive (1,∞) and negative (-∞,1)

• positive (0,∞) and negative (-∞,-1)

• positive (-∞,∞) and negative nowhere

• positive (∞,1) and negative (1,-∞)

Multiple Choice

For what interval is the height of the projectile AT OR ABOVE 120 feet?

• [1, 6]

• [120, 200]

• [0, 7]

• [3, 4]

Multiple Choice

Find the function's maximum and minimum points

• no maximum

  minimum (-4,-1)

• no minimum

  maximum (-3, 1)

• no maximum

  minimum (-1,-4)

• maximum (-3,1)

  minimum (0,-3)

Multiple Choice

What is the location of the relative maximum within the given interval of the graphed function?

 $-5\le x\le0$  

• x = -4

• x = -2

• x = 0

• x = 3

• Does Not Exist

Multiple Choice

What is the location of the absolute maximum for the graphed function?

• x = 1

• x = 3

• x = 4

• x = 5

• Does Not Exist

Multiple Choice

Identify the local minimum

• x = 8

• x = 4

• $\infty$

• x = 2

Multiple Choice

Find the local maximum and minimum

• 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

• $\left(-\infty,\ \infty\right)$

Multiple Choice

Is the function Linear or Nonlinear?

• Linear
• Nonlinear

Multiple Choice

Which of the following intervals has the largest average rate of change?

• [13,14]

• [13, 17]

• [16, 17]

• [16, 19]

Multiple Choice

Find the rate of change.

• -2 minutes per gallon
• -20 minutes per gallon
• -2 gallons per minute
• -20 gallons per minute

Multiple Choice

Use the given function or the graph to find the average rate of change

• -1

• 1

• 1/2

• 2

Multiple Choice

Use the given function or the graph to find the average rate of change

• 5

• -1/5

• -5

• 15

Multiple Choice

Which of the following graphs has the largest average rate of change from -1 to 2?