Pre Calculus Chapter 1

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.

1.1 The Cartesian Plane

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.

Bellwork 8/18

Bellwork 8/18

What type of Symmetry?

What type of Symmetry?

What type of Symmetry?

Try test #1 with: Try test #3 with: Try test #2 with:

Bellwork 8/19

Bellwork 8/19

Find the slope of the line, the y-intercept and sketch a graph of the line.

Find the slope-intercept form of the line

Determine whether the lines are parallel, perpendicular, or neither

𝐿1: (−2 ,−1 ) , (1,5 )𝑎𝑛𝑑𝐿2 (1 ,3 ) ,(5 ,−5)

1.4 Functions

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.

1.5 analyzing graphs of functions

Describe the increasing/decreasing behavior(s)

Describe the increasing/decreasing behavior(s)

Describe the increasing/decreasing behavior(s)

Bell work 8/21

Find the domain:

1.

Find the Zeros of the function.

Bell work 8/21

Find the domain:

1.

Find the Zeros of the function.

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

1.6 Library of Functions

Linear Function

Linear Function

Constant Function

Domain: all Real numbersRange: c

Squaring Function

Squaring Function

Cubic Functions

Cubic Functions

Square Root Function

Square Root Function

Reciprocal Function

Reciprocal Function

Absolute Value Function

Domain: All Real numbersRange: y values greater than or equal to 0Even Function

Bell Work 8/22/14

1.7 Transformation of Functions

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.