Review for Quiz 2.1.1 and 2.1.2

Review for Quiz 2.1.1 and 2.1.2

by Stephanie Balbaneda

​Your quiz will test on the following

• ​Domain and Range

• ​Transformations with Function Notation

• ​Transformations with Piecewise functions

• ​Identifying Piecewise Functions Interval

• ​Title your Notes :

​Chapter 2.1.1 and 2.1.2 NOTES

​Be ready to take notes. Take out your notebook.

​You can use THESE notes for your quiz

​Chapter 2.1.1 and 2.1.2 Notes

​Domain and Range:

​*Watch the following video to take notes

Different notations

• Take the time to read each row

• Notice connections

• The chart is color coded to help you find the connections

​Inequality Graph Interval

​All THREE colums represent the same. Just different notation.

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​Get ready to practice.. You do not need to take notes on the following questions.

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Move on to the next slide

Multiple Choice

What is the range of the graph?

• 1 ≤ x ≤ 5
• 1 < x < 5
• 1 ≤ y ≤ 5
• 1 < y < 5

Multiple Choice

What is the range of the graph?

• -7 ≤ x < 5
• -3 ≤ x < 1
• -3 ≤ y < 1
• -7 ≤ y < 5

Multiple Choice

What is the DOMAIN of this graph?

• -4 ≤ x ≤ 3

• -1 ≤ x ≤ 4

• 4 < x < 3

• -1 < x < 4

Multiple Choice

What is the DOMAIN of this graph?

• x < -3

• x ≤ -3

• x > -3

• x ≥ -3

Multiple Choice

What is the range in inequality notation?

• ( -4 , 4 )

• [ 1 , -3 )

• -4 < x < 4

• 1 ≥ y > -3

Multiple Choice

What is the domain in inequality notation?

• ( -4 , 4 )

• [ 1 , -3 )

• -4 < x < 4

• 1 ≥ y > -3

Multiple Choice

What is the RANGE?

• (-∞, +∞)
• (-2, +∞)
• [-2, +∞)
• (-∞, 0) U (0, +∞)

Multiple Choice

What is the DOMAIN?

• (-∞, +∞)
• (-2, +∞)
• [-2, +∞)
• (-∞, 0) U (0, +∞)

Multiple Choice

What is the RANGE?

• (-∞, +∞)
• (-∞, 1)
• (-∞, 1]
• (-∞, 0) U (0, +∞)

​Chapter 2.1.1 and 2.1.2 Notes

​Domain and Range:

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​*Add a new section to your notes

​Transformations with Function Notations

​Transformations with Function Notations:

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​Here is a shortcut to all the transformations.... Copy them in your notes!

​The next slides are practice:

​You do not need to write them in your notes.

Multiple Choice

• $$𝑦=𝑓(𝑥)+2$$

• $$𝑦=𝑓(𝑥)−2$$

• $$𝑦=𝑓(𝑥+2)$$

• $$𝑦=𝑓(𝑥−2)$$

Multiple Choice

• $$𝑦=𝑓(𝑥)+2$$

• $$𝑦=𝑓(𝑥)−2$$

• $$𝑦=𝑓(𝑥+2)$$

• $$𝑦=𝑓(𝑥−2)$$

Multiple Choice

• $$𝑦=𝑓(𝑥)+3$$

• $$𝑦=𝑓(𝑥)−3$$

• $$𝑦=𝑓(𝑥+3)$$

• $$𝑦=𝑓(𝑥−3)$$

Multiple Choice

• $$𝑦=𝑓(𝑥)+3$$

• $$𝑦=𝑓(𝑥)−3$$

• $$𝑦=𝑓(𝑥+3)$$

• $$𝑦=𝑓(𝑥−3)$$

Multiple Choice

• $$𝑦=𝑓(𝑥+5)+3$$

• $$𝑦=𝑓(𝑥−5)−3$$

• $$𝑦=𝑓(𝑥+5)−3$$

• $$𝑦=𝑓(𝑥−5)+3$$

Multiple Choice

• $$𝑦=𝑓(2𝑥)$$

• $$𝑦=𝑓(1/2𝑥)$$

• $$𝑦=2𝑓(𝑥)$$

• $$𝑦=1/2𝑓(𝑥)$$

Multiple Choice

Which transformation will occur if f(x) = x² is replaced with 2⋅f(x)?

• Vertical Compression by a factor of 2
• Vertical Stretch by a factor of 2
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Multiple Choice

Which of the following transformations are present?
-2f(x - 1) + 2

• Shift 1 unit down
• Shift 1 unit up
• Shift 1 unit left
• Shift 1 unit right

Multiple Choice

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

• f(x + 3) - 4
• f(x - 4) + 3
• f(x + 4) + 3
• f(x + 3) + 4

Multiple Choice

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

• f(x + 2)
• f(x) + 2
• f(x - 2)
• f(x) - 2

Multiple Choice

If $$f\left(x\right)=2x-1$$  

Find an expression for  $$f\left(x\right)+4$$  

• $$2x+3$$  

• $$x+4$$  

• $$2x-4$$  

Multiple Choice

If $$f\left(x\right)=2x-1$$  

Find an expression for  $$f\left(2x\right)$$  

• $$2x+4$$  

• $$4x$$  

• $$4x-1$$  

​Transformations with Function Notations:

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​Transformations with PIECEWISE Functions :

​Add the next section to your notes

​Transformations with PIECEWISE Functions

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​watch the following videos to take notes

Multiple Choice

Write the equation for g(x) if g(x) = f ( x+2) - 4

• $$\left(x+2\right)^2-5,\ x\le0$$   $$2x-1\ ,\ 0<x<5$$  

  $$-1,\ x>5$$  

• $$\left(x+2\right)^2-5,\ x\le-2\ \ \$$   $$2x-1\ ,\ -2<x<3$$  

• $$x^2+2-5,\ x\le2$$  

  $$2x-2,\ 0\le x\le4$$  

• $$\left(x-4\right)^2-2,\ x\le0$$   $$2x-4\ +2,\ 0<x\le2$$  

Multiple Choice

What is f(0)?

• 5

• 3

• 2x+3

• 5x

• none of these are correct

Multiple Choice

Which piecewise function corresponds to this graph? (Take your time)

• f(x) = { x  if x < 4;   -x+1  if x ≥ 4
• f(x) = { x  if x ≤ 4;  -x+1  if x > 4
• f(x) = { -x+1  if x < 4;  x  if x ≥ 4
• f(x) = { -x+1  if x ≤ 4;  x if x > 4

Multiple Choice

Match the graph with the correct equation.

Multiple Choice

Find f(2)

• f(2) = 0

• f(2) = 1

• f(2) = 3

• f(2) = 4