1. Name:__________ warm-up 9-7
Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. {(–3, 4), (–2, 1), (–1, 0), (0, 1), (1, 4)}
Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. {(3, –18), (4, –14), (5, –10), (6, –6), (7, –2)}

2. Look for a pattern in each table of values to determine which kind of model best describes the data.

3. Details of the Day Activities: EQ:
What type of graph does a quadratic equation graph into?
What type of information can you derive from the graph?
I will be able to…
Identify and graph step functions.
Identify and graph absolute value and piecewise-defined functions.
Activities:
Warm-up
Review homework
Notes:
Class work/ HW
Vocabulary:
step function
piecewise-linear function
greatest integer function
absolute value function
piecewise-defined function .

4. 9-7 Special Functions
An absolute value function can be represented by a piecewise function, with two domain sections. One section of the domain of the piecewise function will represent the portion of the absolute value function with a negative slope, while the other section of the domain of the piecewise function will represent the portion of the absolute value function with a positive slope.
Just as an absolute value function has characteristics, such as a vertex, axis of symmetry, and maximum/minimum, a piecewise function can possess these characteristics as well.
Remember that the graph of a piecewise function, which represents an absolute value function, is "V"-shaped. This "V"-shaped graph is symmetric about a line, known as the axis of symmetry, and it can open up or down.
If the graph of a piecewise function, which represents an absolute value function, opens up, then the function has a minimum value at its vertex.
If the graph of a piecewise function, which represents an absolute value function, opens down, then the function has a maximum value at its vertex.
A piecewise function is a function defined by two or more expressions, where each expression is associated with a unique interval of the function's domain.
Discontinuities of a function are points where the graph of a function has breaks or gaps
The domain of a function is the set of all possible real input values, usually represented by x.
The range of a function is the set of all possible real output values, usually represented by y.

5. A Quick Review
Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. {(–3, 4), (–2, 1), (–1, 0), (0, 1), (1, 4)}
Graph each set of ordered pairs. Determine whether the ordered pairs represent a linear function, a quadratic function, or an exponential function. {(3, –18), (4, –14), (5, –10), (6, –6), (7, –2)}

6. A Quick Review
Look for a pattern in each table of values to determine which kind of model best describes the data.

7. Notes and examples

8. Notes and examples X
X + 3
[[X+3]]

9. Notes and examples
A taxi company charges a fee for waiting at a rate of $0.75 per minute or any fraction thereof. Draw a graph that represents this situation. X
F(X)

10. Notes and examples
SHOPPING An on-line catalog company charges for shipping based upon the weight of the item being shipped. The company charges $4.75 for each pound or any fraction thereof. Draw a graph of this situation. X
f(X)

11. Notes and examples X
f(X)

12. Notes and examples Graph f(x) = │2x + 2│. State the domain and range X

13. Notes and examples X
f(X)

14. Notes and examples X
f(X) X
f(X)

15. Notes and examples X
f(X) X
f(X)

16. Notes and examples

17. Notes and examples . X
f(X)

18. Notes and examples X
f(X)

19. Notes and examples X
f(X) X
f(X)

20. Notes and examples X
f(X) X
f(X)