Chapter 5 Review Relations and Functions Coordinate Plane

Chapter 5 Review Relations and Functions

Coordinate Plane Label these: X Axis Y Axis Quadrant I Origin II IV

Coordinates are written (x, y) Which Quadrant is point N in? Point S?

Chapter 5 -2 Domain and Range Domain: all of the x values Range: all of the y values

Chapter 5 -2 Functions What is a function? A relation that assigns exactly one value in the range to each value in the domain I. E. Every X value has only one Y value 2 tests that can be used to see if a relation is a function: 1) For a list of ordered pairs, make sure there are no repeating X values 2) For a graph, use the Vertical Line Test

Is it a Function? Identify the Domain and the Range. Determine if the relation is a function {(-2, -1), (-1, 0), (6, 2), (6, 3), (2, 1)} {(6. 5, 0), (7, -1), (6, 2), (2, 6), (-6. 5, -1)}

Is it a Function?

Chapter 5 -2 Evaluating Functions Evaluate f(x) = 3 x -5 for x= -2 Evaluate f(b) = b 2 + 1 for b= 3

Chapter 5 -3 Graphing Functions Graph the following functions using and input/output table. 1. f(x) = - x + 4 x f(x) 2. f(x) = |x | + 4

Chapter 5 -3 Graphing Functions 3. f(x) = |x - 4| 4. f(x) = x 2 + 4

Chapter 5 -4 Writing Rules for Functions Step: 1. Find a pattern. Think, “how did they get from x to y? ” 2. Write an equation from the pattern. 3. Check the equation for a couple of domain values. 1. x 1 2 3 4 y 5 6 7 8 y=x+4 2. x 1 2 3 4 y 2 4 6 8 y = 2 x 3. x 1 3 f(x) 1 9 6 9 36 81 f(x) = x 2

Chapter 5 -4 Writing Rules for Functions Step: 1. Define your variables (2). 2. Write an equation according to the situation. 3. Check the equation. Write a function rule for each situation. The total cost t(c) of c ounces of cinnamon if each ounce costs $. 79 t(c) = total cost c = ounces t(c) = $. 79 c

Chapter 5 -4 Writing Rules for Functions Step: 1. Define your variables (2). 2. Write an equation according to the situation. 3. Check the equation. Write a function rule for each situation. The area A (n) of a square when you know the length n of a side. A(n) = area of sqaure n = length of side A (n) = n 2

Word Problem A donut costs 75 cents. a. Write a function rule to describe how the amount of money M needed to buy n number of donuts. b. Make a table of values showing how much it would cost to buy 4 different amounts of donuts c. Graph the function

Chapter 5 -6 Number Paterns Inductive reasoning: making conclusions based on patterns you observe. A number pattern is also called a sequence

Chapter 5 -6 Finding Common Difference What does “common difference” mean? how much to add to get to the next number