Integrated 3 Review Unit 2
This is a summary review for Integrated 3 Unit 2 Test. The test will be worth 100 points. There will be problems from each of the following sections.

2-1 What is a function?

What is a function?	How do you read f(x) = x?	Solve C(r) = 2πr for r = 4
Solve f(x) = 2x^2 + 3 for x = 2	Solve: f(x) = (x + 2)^2 for x = 3	Solve f(x) = 2x^2 - 12 for x = 4
Solve f(x) = 3x^2 - 1 for x = a	Solve: f(x) = (x + 2)^2 for x = a + b	Solve: f(x) = (x + 2)^3 for x = 5
Is a sine wave a function?	Is a parabola with the opening facing up a function?	Is a parabola with the opening facing right a function?

2-2 Linear Functions

What is the generic formula for a linear function?	Solve f(x) = ^1/3x +10 for f(9)	Solve f(x) = ^1/3x +10 for f(x)=12
Is a parabola a linear function?	Is a horizontal line a linear function?	Is a vertical line a linear function?
What is the definition of a linear function?	Create a linear function that goes through the following two points: (5,6) and (3,2).	Create a linear function that goes through the following two points: (7,2) and (2,12).
Create a linear function that goes through the following two points: (0,6) and (3,2).	Create a linear function that goes through the following two points: (7,2) and (6,4).	Create a linear function that goes through the following two points: (8,2) and (4,4).
Solve f(x) = -3x + 2 for x = 3	Solve f(x) = -3x + 2 for x = -6	Solve f(x) = -3x + 2 for x = a + b
Solve f(x) = 5x - 2 for x = 3	Solve f(x) = 5x - 2 for x = -6	Solve f(x) = 5x - 2 for x = a + b

2-3 Piecewise and Absolute Value Functions

Graph the Following:

What is a piecewise function?	What is an absolute value function?	How can light reflection and refraction be described by these two types of formulas?
0 if 0 ≤ x < 4 f(x) = 2 if 4 ≤ x < 8 2x –2 if 8 ≤ x < 12 20 if 12 ≤ x	x if 0 ≤ x < 4 f(x) = -x + 8 if 4 ≤ x < 8 x - -8 if 8 ≤ x < 12 -x + 16 if 12 ≤ x	f(x) = | x |
Look at page 91 and go through the billiard problem again.	f(x) = -|x^2|	f(x) = x if 0 ≤ x < 10 10 if 10 ≤ x
Graph and find the function definitions for the following lines between the following points: 1. (0,5) to (5,0), 2. (5,0) to (8,3), 3. (8,3) to (11,0), 4. (11,0) to (16,5)	Graph and find the function definitions for the following lines between the following points: 1. (0,0) to (5,10), 2. (5,10) to (10,10)	Graph and find the function definitions for the following lines between the following points: 1. (0,5) to (5,5), 2. (5,5) to (10,10)
Graph f(x) = |5x –2|	Graph f(x) = |-2x + 5|	Graph f(x) = |2x –4|

2-4 Quadratic Functions

What is a quadratic function?	What is the quadratic equation?	How do you solve where a thrown ball will pass certain heights?
Work through problem 11 on page 98	Derive quadratic equation from formula: ax^2 + bx + c = 0	Solve for x if 5x^2 + 2x - 7 = 0
Solve for x if 5x^2 + 2x +1 = 10	Solve for x if x^2 - 2x +1 = -23	If a person throws a baseball at 150 ft/sec from 6 feet at an angle of 15^o, when will the ball hit the ground?
Use quadratic equation to solve: 10x^2 + 3x +1 = 10	Create a formula using x if f(0)=2, f(2)=6, and f(4)=18	Create a formula using x if f(0)=3, f(2)=17, and f(4)=47

2-5 Polynomial Functions

What is a polynomial function?	How can you tell a even polynomial equation from an odd polynomial equation?	What happens when the coefficient of the highest power is positive? Is negative?
Work through problem 11 on page 104	Solve f(x) = 3x^3 –2x^2 +x –2 for x = 3	Graph f(x) = 0.3x^3 –0.2x^2 +x –2

2-6 Radical Functions

What is a radical function?	How do you solve a radical function?
Solve problem 17 on page 114	Solve f(x) = 2 square root of (3x) for x = 12	Solve Square root of x = 4x
Graph: f(x) = 2 times square root of (x^4-2)	Solve Square root of (x + 6) = x	What is a radical function?
Simplify fourth root of (-3)^4	Simplify fifth root of (-3)^5	Solve f(x) = 3 square root (x+4) if x = 2
Compare square root of (-4)(-16) to square root of (-4) times square root of (-16)	Solve f(x) = square root of (4x+2) for x=7	Solve f(x) = 3 square root of (x^4) for x=3

2-7 Rational Functions

What is a rational function?	What is a rational expression?	Graph f(x) = (x2 –2x +5)/(x –1)
Graph f(x) = 4/(x-2)	Graph f(x) = 1/(-4x^2 + 2)	Graph f(x) = x/(2x^2 +2)
Solve & Graph: f(x)=x/(2x-1)	Solve & Graph: f(x)=x^2/(2x-1)	Solve & Graph: f(x)=2x/(x-1)

2-8 Combining Functions

What is a combination function?	How do you solve a combination function?	Why do you combine functions?
How do you say g(f(x))?	How do you say (g^of)(x)?	For h(x)=square root of (x^2+3), g(x) = x^2 +3x – 4, and f(x)=3x find the following composite functions.
(g^of)(x)	(g^oh)(x)	(f^og)(x)
(f^oh)(x)	(h^og)(x)	(h^of)(x)