Pre Calculus Chapter 1. Some Classroom rules 1.No food in this classroom. 2.Drinks must have caps....
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Transcript of Pre Calculus Chapter 1. Some Classroom rules 1.No food in this classroom. 2.Drinks must have caps....
Some Classroom rules 1. No food in this classroom. 2. Drinks must have caps. (bottled water is fine) A soft drink with a lid is not
allowed. 3. Come to class with all of your materials. Pen/pencil, paper, and a calculator.
You may not leave class to retrieve these materials from another classroom.4. Treat those around you with respect. Vulgar or profane language will earn
you a referral. Any language used to belittle another student may be grounds for suspension.
5. No cell phone use.6. If we are using technology, you must use the device as prescribed. No games
or Facebook, etc.
How important was the picture to solving this problem? Think about that when you have to solve word problems in the future that don’t include a picture/diagram.
1.2 Graphs of Functions
Understanding the graph of an equation can help in determining that the input-output relationship is going as planned.
Determine whether the lines are parallel, perpendicular, or neither
𝐿1: (−2 ,−1 ) , (1,5 )𝑎𝑛𝑑𝐿2 (1 ,3 ) ,(5 ,−5)
Bell work 8/20
Find the domain:
1.
Determine if the following has symmetry to the x-axis, y-axis, with respect to the origin, or none of these.
Guess my graph exercise
1. Pair up.2. One person has a blank graph that
they must complete.3. The other has the graph that they
must describe to their partner.4. When describing the graph, be sure
to use the key words:Increasing, decreasing, maximum, minimum, smooth turn, sharp turn
Questions:
1. How do you find the average of two numbers?
2. What is the average of 5 and 7?
3. Does that change if we add more context to the problem? For example, what is the average speed given 5fps and 7fps?
4. Now let’s say that 5fps was observed at 4 minutes and 7fps was observed at 10 minutes. Is the average speed still the same?
The average rate of change between any two points and is the slope of the line through the two points. The line through the two points is called the secant line, and the slope of this line is denoted as
Absolute Value Function
Domain: All Real numbersRange: y values greater than or equal to 0Even Function
Horizontal/Vertical Shifts
f(x) Shift 3 Units upf(x)+3
Shift 3 Units Rightf(x-3)
Shift 3 Units Leftf(x+3)
2)( xxf 3)( 2 xxf 2)3()( xxf2)3()( xxf
xxf )(
xxf )(
3)( xxf 3)( xxf 3)( xxf
3)( xxf 3)( xxf 3)( xxf
Horizontal/Vertical Shifts
f(x) Shift 3 Units upf(x)+3
Shift 3 Units Rightf(x-3)
Shift 3 Units Leftf(x+3)
xxf 2)(
•Rigid transformations = Transformations that do not change the shape of the graph. Reflections and shifts are rigid transformations.•Non-rigid transformations = transformations that
change the shape of the graph. Vertical Stretch, Horizontal Stretch, Vertical Shrink, and horizontal shrink are examples of non-rigid transformations.