1. Write each using Interval Notation. Write the domain of each function.
Students, Take out your calendar and your homework. Take out your spiral notebook and Complete the DNA. Use your notes if necessary.
Write each using Interval Notation.
Write the domain of each function. 1) -3 9

2. Determine the values of x where the function in increasing, decreasing, and constant.

3. Vertical and Horizontal Shifts

5. Use the graph of
to graph the following functions.

6. Use a graphing utility to compare the functions.

7. Given that the parent function of the graph to the right is
Write the equation of the function.

8. Reflecting Graphs
Example

9. Determine the relative minima and maxima of the following function
Determine the relative minima and maxima of the following function. Determine where the graph is increasing, decreasing, and constant.

10. Relative maximum
Relative minimum
Relative maximum
Relative minimum

11. Find the domain of the functions.

13. Piecewise-Defined Functions
A piecewise-defined function is composed of two or more functions.
f(x) =
3 + x, x < 0
x2 + 1, x 0
Use when the value of x is less than 0.
Use when the value of x is greater or equal to 0. x y 4 -4
open circle
closed circle
(0 is not included.)
(0 is included.)
Piecewise-Defined Functions

14. f (x) = x2 is an even function.
A function f is even if for each x in the domain of f, f (– x) = f (x).
Symmetric with respect to the y-axis. x y
f (x) = x2
f (– x) = (– x)2 = x2 = f (x)
f (x) = x2 is an even function.
Even Functions

15. f (x) = x3 is an odd function.
A function f is odd if for each x in the domain of f, f (– x) = – f (x).
f (x) = x3 x y
f (– x) = (– x)3 = –x3 = – f (x)
Symmetric with respect to the origin.
f (x) = x3 is an odd function.
Odd Functions

16. Now we are going to graph the piecewise function from DNA #4-6 by HAND.

17. This graph does not pass the vertical line test. It is not a function.
A relation is a function if no vertical line intersects its graph in more than one point. x y 4 -4 x y 4 -4
x = | y – 2|
y = x – 1
This graph does not pass the vertical line test. It is not a function.
This graph passes the vertical line test. It is a function.
Vertical Line Test

18. Graph this…