Homework LogTues

11/10

Lesson Rev

Learning Objective: To remember everything in Chapter 3!

Hw: #309 Pg. 206 #1 – 4, 8, 12, 20 – 25, 27 – 34, 37 – 39, 42, 45, 47, 50, 53, 57

Homework LogFri

11/13

Lesson Rev

Learning Objective: To remember everything in Chapter 3!

Hw: Quiz Correction

Homework LogFri

11/13

Lesson Rev

Learning Objective: To remember everything in Chapter 3!

Hw: Extra Credit Review WS

11/10/15 Chapter 3 ReviewAdvanced Math/Trig

Learning Objective

To remember everything in Chapter 3!

Graph1.

a = –1 Opens down

Vertex: (1, 5)

AoS: x = 1

Max

Max Value of 5

x y

–1

0

1

4

2

3

4

1

V( 1 5)

Extreme Value2. Find the Extreme Value and state whether that value represents a max or min.

a = 2 Opens up = f() = Extreme Value is 1 which is a min

Piecewise Function3. Graph Closed Circle @ x = –2

Open Circle @ x = –2

, ,

x y x y

–2

–3

–4

4

4.5

5

–2

–1

0

3

2

1

Piecewise Function4. Graph Open Circle @ x = –1

Closed Circle @ x = –1 , ,

x y x y

–1

–2

–3

3

1

–1

–1

0

1

4

3

2

Write a Linear Equation

5. Write an equation in Standard Form of the line through (–2, 6) and perpendicular to 5x – 3y = 12Find slope of 5x – 3y = 12 Perpendicular slope = 5y – 30 = – 3(x + 2)5y – 30 = –3x – 63x + 5y = 24

23

Or get into slope-intercept form

5x – 3y = 12

– 3y = – 5x + 12

y =

Write a Linear Equation

6. Write an equation in Standard Form of the line with x-intercept 7 and parallel to 6x – 9 = 3y

Parallel slope = 2

Point (7, 0)

y – 0 = 2(x – 7)

y = 2x – 14

2x – y = 1423

Get into slope-intercept form

6x – 9 = 3y

y = 2x – 3

Write an equation in standard form

7. y-intercept: 6 and x-intercept: –2

(0, 6) & (–2, 0)

y – 0 = 3(x + 2)

y = 3x + 6

3x – y =– 6

Or you already know the slope and y-intercept

y= mx + b

y = 3x + 6

3x – y = –623

Composite Functions8.

x

= g(

1

=

=

Composite Functions9.

x

= f(3x+1

=

=

Functions10. Find domain of f and g x – 2 0and 7 – x 0x 2 and – x – 7x 2 and x 7

Domain of f and g is where they overlap!!2 7

[2, 7]

+

Functions10.

x [2, 7]x [2, 7]x [2, 7]x [2, 7) x

y

x

Warm – up #4 11. Graph

1.01.21.92.02.22.93.0

x y

–2–2–2–1–1–10

12. Vertex: (–2, 4)

x y

V(– 2 4)

– 4 – 3

– 1 0

2 3

3 2

Is a function.

Passes the vertical line test.

D:

R:

13. Vertex: (1, 0)

x y

V(1 0)

– 1 0

2 3

4 1

1 4

x = = 1

y =

Is a function.

Passes the vertical line test.

D:

R:

Find the Difference Quotient

14.

=

=

=

= =

Function15. Find domain & range and determine if the relation is a function. {(–1, –2), (–3, 4), (–1, 0)}

Domain: {–1, –3}

Range: {–2, 0, 4}

Not a function because x = –1 twice with different y – values

b. Find g (–3) = – 3(–3) = 2(9) + 9= 27

a. Find f (–3) = 3(–3) – 7 = – 16

Find Function Values16.

c. Find f (g (–3)) = 3(27) – 7 = 74

Find Domain & Range17. Domain – x +5 0 x

Range will also come out 0 y 0

Word Problem18. The cost (in dollars) of operating a pizza delivery car is given by C = 9000 + 0.5x, where x is the number of miles that the car is driven. Use appropriate restrictions on the variable & graph this equation.

Cost (y) won’t go below 0, depends on miles (x), which also won’t go below 0.

Graph by finding y – intercept & x – intercept.

#18 continued18. C = 9000 + 0.5x

(0, 9000) & (–18000, 0)

Don’t have graph on Quadrant II 9000

–18000 milesC

ost

Applying Slope19. Suppose 3 points (0, 0), (1, 2), and (3, y) lie on a straight line. Find the missing coordinate.

Find slope = =

Use slope and other set of points to solve

= =

1(y – 2) = 2(2)

y – 2 = 4

y = 6

Make a table and plug values into y and

solve for xy

x

Sketch the graph

│–2│– 2

│–1│ – 2

│0│ – 2

│1│ – 2

│2│ – 2

–2

–1

0

1

2

0

–1

–2

–1

0

x │y│ – 1 y

20.

Midpoint Formula

1 1 2 2

1 2 1 2

Given ( , ) , ( , )

Find the midpoint

,2 2

x y x y

x x y y

y

x

Two Special Cases

x = -3 (no y)

y = 2 (no x)I only see an

“x” It

goes thru

x-axis

I only see a “y”

It goes thru y-

axis

y

x

Vertical line thru (-3, 0)

Undefined Slope

Horizontal line thru

(0, 2)Zero Slope

ZeroUndefined

Finding Domain of an Equation

Domain: Look for any restrictions on x

(y must be real)

x under radical

x in denominator of a fraction

Finding Range of an Equation

Range: Look for any restrictions on y

(using known domain)

y = y 0

y 0

y = y 0

y = y 0

Draw a quick sketch if need

to or use graphing calculator

Homework

#309 Pg. 206 #1 – 4, 8, 12, 20 – 25,

27 – 34, 37 – 39, 42, 45, 47, 50, 53, 57