# SpecialFunctionsLesson

Created 2 years ago

Duration 0:00:00
49
Slide Content
1. ### Slide 1

• Special Functions:
• Step, Absolute Value, and Piecewise Functions
2. ### Slide 2

• Ponder This…
• Suppose you took the advice of these guys and bought a ton of Duct Tape to fix everything that ails for life. If they come in 100-foot rolls, can we find a function that takes the length of duct tape needed as our input and outputs how many rolls to buy? What would such a graph look like when graphed?
3. ### Slide 3

• Ponder This…
• This is what our duct-tape function looks like. (What do we need to be careful about here to make sure it is a function?)
• We have never seen anything like this before! What witchery is this? Today, we will find out!
4. ### Slide 4 - CCSS

• Content Standards
• F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
• F.IF.7b Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
• Mathematical Practices
• 4 Model with mathematics.

6. ### Slide 6 - Concept

• This is a graph of the greatest integer function. In this graph, y is equal to the greatest integer value of x. So, if x = 5.5, y = 5. Drag the slider to change the value of the green point on this function. 1. What happens when the green point approaches the open points? The closed points?2. Can x and y both be integers?3. Is y ever greater than x?4. Could you trace this graph without picking your pencil up off a piece of paper?5. How would you descibe this graph to someone else?
• T. I.P.S.!!!
• TIME:
• 7 MIN
7. ### Slide 7 - Example 1

• Greatest Integer Function
• First, make a table of values. Select a few values between integers. On the graph, dots represent points that are included. Circles represent points that are not included.
8. ### Slide 8 - Example 1

• Greatest Integer Function
• First, make a table of values. Select a few values between integers. On the graph, dots represent points that are included. Circles represent points that are not included.
9. ### Slide 9 - Example 1

• Greatest Integer Function
• First, make a table of values. Select a few values between integers. On the graph, dots represent points that are included. Circles represent points that are not included.
• Answer: Because the dots and circles overlap, the domain is all real numbers. The range is all integers.
10. ### Slide 10 - Example 1

• A. D = all real numbers, R = all real numbers
• B. D = all integers, R = all integers
• C. D = all real numbers, R = all integers
• D. D = all integers, R = all real numbers
11. ### Slide 11 - Example 1

• A. D = all real numbers, R = all real numbers
• B. D = all integers, R = all integers
• C. D = all real numbers, R = all integers
• D. D = all integers, R = all real numbers
12. ### Slide 12 - Example 1

• A. D = all real numbers, R = all real numbers
• B. D = all integers, R = all integers
• C. D = all real numbers, R = all integers
• D. D = all integers, R = all real numbers
13. ### Slide 13 - Concept

• Check It Out!

15. ### Slide 15 - Example 3

• A. D = all real numbers, R = all numbers ≥ 0
• B. D = all numbers ≥ 0R = all real numbers,
• D = all numbers ≥ 0, R = all numbers ≥ 0
• D = all real numbers, R = all real numbers
• Graph f(x) = │x + 3│. State the domain and range.
16. ### Slide 16 - Example 3

• A. D = all real numbers, R = all numbers ≥ 0
• B. D = all numbers ≥ 0R = all real numbers,
• D = all numbers ≥ 0, R = all numbers ≥ 0
• D = all real numbers, R = all real numbers
• Graph f(x) = │x + 3│. State the domain and range.
17. ### Slide 17 - Example 3

• A. D = all real numbers, R = all numbers ≥ 0
• B. D = all numbers ≥ 0R = all real numbers,
• D = all numbers ≥ 0, R = all numbers ≥ 0
• D = all real numbers, R = all real numbers
• Graph f(x) = │x + 3│. State the domain and range.
18. ### Slide 18 - Concept

• Check It Out!
19. ### Slide 19 - Example 4

• Piecewise-Defined Function
20. ### Slide 20 - Example 4

• Piecewise-Defined Function
• Graph the first expression. Create a table of values for when x < 0, f(x) = –x, and draw the graph. Since x is not equal to 0, place a circle at (0, 0).
• Next, graph the second expression. Create a table of values for when x ≥ 0, f(x) = –x + 2, and draw the graph. Since x is equal to 0, place a dot at (0, 2).
21. ### Slide 21 - Example 4

• Piecewise-Defined Function
22. ### Slide 22 - Example 4

• Piecewise-Defined Function
• D = all real numbers, R = all real numbers
23. ### Slide 23 - Concept

• T. I.P.S.!!!
• TIME:
• 5 MIN
24. ### Slide 24 - Example 4

• D = y│y ≤ –2, y > 2, R = all real numbers
• D = all real numbers,R = y│y ≤ –2, y > 2
• D = all real numbers,R = y│y < –2, y ≥ 2
• D. D = all real numbers,R = y│y ≤ 2, y > –2
25. ### Slide 25 - Example 4

• D = y│y ≤ –2, y > 2, R = all real numbers
• D = all real numbers,R = y│y ≤ –2, y > 2
• D = all real numbers,R = y│y < –2, y ≥ 2
• D. D = all real numbers,R = y│y ≤ 2, y > –2
26. ### Slide 26 - Example 4

• D = y│y ≤ –2, y > 2, R = all real numbers
• D = all real numbers,R = y│y ≤ –2, y > 2
• D = all real numbers,R = y│y < –2, y ≥ 2
• D. D = all real numbers,R = y│y ≤ 2, y > –2
27. ### Slide 27 - Concept

• Check It Out!