Algebra II

​Algebra 2 Review:

Piecewise-Defined Functions

10 total questions​

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Have fun and be safe :)​

​

Poll

Rate your current state of understanding of the learning target.

Learning Target: I can apply my knowledge of piecewise-defined functions to solve problems

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there

• 1 - I don't understand, I need some more help.

​Piecewise-Defined Functions

Use your notes packet to help you!

Let's review!

There are a total 10 questions. Use your piecewise-defined function notes packet to help you if you need!

Multiple Choice

1. Identify the domain and range of the absolute value function  $$f\left(x\right)=\left|x\right|$$  .

• Domain: {0, 1, 2, 3, 4}.

  Range: {0, -1, -2, -3, -4}

• Domain: {-4, 4}.

  Range: {-4, 4}

• Domain: All real numbers Range:  $$\left(0,\infty\right)$$   

• Domain: All real numbers
  Range: All real numbers

Multiple Choice

2. Jay rides in a boat from his home to his friend’s home in a neighboring state. The graph of the function 𝙙(𝙩) = 𝟯𝟬|𝙩 − 𝟭.𝟱| shows the distance of the boat in miles from the state line at t hours. Assume the graph shows Jay's entire trip.

 How far does Jay travel to visit his friend?

• 90 miles

• 40 miles

• 45 miles
  

• 2.5 miles

Multiple Choice

3. A cyclist competing in a race rides past a water station. The graph of the function 𝘥(𝘵)=𝟣𝟥|𝘵−𝟨𝟢| shows her distance from the water station at t minutes. Assume the graph represents the entire race. 

How long does it take the cyclist to make it to the WATER STATION?

• 20 minutes

• 60 minutes

• 105 minutes
  

• 120 minutes

Multiple Choice

4. Jay rides in a boat from his home to his friend’s home in a neighboring state. The graph of the function 𝙙(𝙩)=𝟯𝟬|𝙩−𝟭.𝟱| shows the distance of the boat in miles from the state line at t hours. 

What is the rate of change (the speed of the boat) over the interval 𝟮 ≤ 𝙩 ≤ 𝟮.𝟱?

Use the slope formula  $$m=\frac{y_2-y_1}{x_2-x_1}$$  for the points (2, 15) and (2.5, 30).

• 15 mi/hr

• 20 mi/hr

• 30 mi/hr
  

• 45 mi/hr

Multiple Choice

5. What is the rate of change  over the interval 15 ≤ x ≤ 18?

Use the slope formula  $$m=\frac{y_2-y_1}{x_2-x_1}$$  for the points (15, 3) and (18, 5).

• 0.6

• 0.75

• 1.5
  

• 2

Great work so far!

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Multiple Choice

6. Express 𝘧 (𝘹) = − 𝟥|𝘹 | as a piecewise-defined function.

• $$-3x,\ x\ <\ 0$$  

  $$-3x,\ x>0$$  

• $$3x,\ x\ge0$$   $$-3x,\ x\le0$$  

• $$-3x,\ x\ge0$$  

  $$3x,\ x<0$$  

Multiple Choice

7. Over what part of the domain is the function increasing? Decreasing?

• Increasing: All real numbers
  Decreasing: x > 2

• Increasing:  $$x\le2$$  

  Decreasing:  $$x>2$$  

• Increasing:  $$x\ge2$$  

  Decreasing:  $$x\le2$$  

Multiple Choice

8. If I use 8 gallons of water, will I be charged the rate from Tier 1, 2, or 3?

• 1

• 2

• 3

Multiple Choice

9. According to the piecewise-defined function, which is the cheapest option?

a. One order of 200 wristbands: f(200)  b. Two orders of 100 wristbands each: 2f(100)  c. Four orders of 50 wristbands each: 4f(50)

• f(200)

• 2f(100) 

  
  

• 4f(50)

  
  

• They are all the same.

Multiple Choice

10. What is the range (the y-value) for the domain interval  $$1.5\le x<2.5$$  ?

• 4

• 3

• 2

  
  

• 1

Poll

Rate your current state of understanding of the learning target.

Learning Target: I can apply my knowledge of piecewise-defined functions to solve problems.

• 4 - I can teach it!

• 3 - I understand it.

• 2 - I'm getting there

• 1 - I don't understand, I need some more help.