Pre-Algebra Unit 2

Graphs and Functions

Name: ___________________________ Period: _______

Common Core State Standards CC.8.F.1 - Understand that a function is a rule that assigns to each input exactly one output.

The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

CC.8.F.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

CC.8.F.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Scope and Sequence Day 1 Lesson 2-1 Day 7 Lesson 2-4

Day 2 Lesson 2-2 Day 8 Lesson 2-5

Day 3 Tech Lab Day 9 Lesson 2-5

Day 4 Lesson 2-3 Day 10 Tech Lab

Day 5 Quiz Day 11 Review

Day 6 Lesson 2-4 Day 12 Test

IXL Modules SMART Score of 80 is required

Due the day of the exam

Lesson 1 8.X.2 Does (x, y) satisfy the linear function?

8.U.1 Find the solution from a set

Lesson 2 8.P.1 Points on coordinate graphs

8.P.2 Quadrants and axes

8.P.3 Coordinate graphs as maps

7.P.4 Distance between two points

Lesson 3 8.AA.4 Interpret line graphs

8.AA.5 Create line graphs

Lesson 4-5 8.X.7 Complete a table for a linear function

8.X.1 Identify functions

8.X.8 Graph a line from a function table

Lesson 2-1

Ordered Pairs

Warm-Up

An ordered pair (x, y) is a pair of numbers that can be used to locate a ____________

on a ____________ ____________. A solution of a two-variable equation can be

written as an ordered pair.

Examples: Deciding Whether an Ordered Pair is a Solution of an Equation

Determine whether each ordered pair is a solution of y = 4x - 1. (3, 11)

Determine whether each ordered pair is a solution of y = 4x - 1. (10, 3)

Determine whether each ordered pair is a solution of y = 5x + 3. (7, 38)

Determine whether each ordered pair is a solution of y = 4x - 1. (9, 17)

Examples: Creating a Table of Ordered Pair Solutions

Use the given values to make a table of solutions. y = x + 3 for x = 1, 2, 3, 4

n = 6m - 5 for m = 1, 2, 3

y = x + 6 for x = 1, 2, 3, 4

n = 8m - 2 for m = 1, 2, 3, 4

Examples: Consumer Math Application

A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost. What will be the sales price of a sweater with a wholesale cost of $48?

A salesman marks up the price of everything he sells by 20%. The equation for the sales price p is p = 1.2w, where w is wholesale cost. What will be the sales price of a jacket with a wholesale cost of $85?

In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7.5%, the equation for total cost is c = 1.075p, where p is the price before tax. How much will a $22 item cost after sales tax?

In most states, the price of each item is not the total cost. Sales tax must be added. If sales tax is 7.5%, the equation for total cost is c = 1.075p, where p is the price before tax. How much will a $10 item cost after sales tax?

Lesson 2-2

Graphing on a Coordinate Plane

Warm-Up

The coordinate plane is formed by two ____________ ____________, the x-axis and the

y-axis. They intersect at right angles and divide the plane into ____________ quadrants.

The x-coordinate is the ____________ number in an ordered pair. The y-coordinate is the

____________ number in an ordered pair.

To plot an ordered pair, begin at the origin, the point (0, 0). It is the ____________ of the

x-axis and the y-axis.

The x-coordinate tells how many units to move ____________ or ____________; the

y-coordinate tells us how many units to move ____________ or ____________.

Examples: Graphing on a Coordinate Plane

Give the coordinates and quadrants of each point.

Point R is: ____________________ Point S is: ____________________ Point T is: ____________________ Point U is: ____________________

Point J is: ____________________ Point M is: ____________________ Point K is: ____________________ Point P is: ____________________

Examples: Graphing Points on a Coordinate Plane

Graph each point on the coordinate plane.

A. A(3, 4) B. B(4, 0) C. C(-4, 4) D. D(-1, -3)

A. A(2, 4) B. B(2, 0) C. C(-2, 4) D. D(-1, -1)

Examples: Finding the Horizontal and Vertical Distances

Find the distance between each pair of points.

A. K and L B. M and N

A. A and B B. C and D

Lesson 2-3

Interpreting Graphs

Warm-Up

Examples: Matching Situations to Graphs

Examples: Creating a Graph of a Situation

Create a graph for each situation. Tell whether the graph is continuous or discrete.

This table shows the temperature inside a car over time.

This table shows the distance traveled during a family vacation.

Lesson 2-4

Functions

Warm-Up

A set of ordered pairs is a relation. The domain of a relation is the set of ______ values of the ordered pairs. The range of a relation is the set of ______ values of the ordered pairs. A function is a special type of relation that pairs each ____________, or domain value with exactly one ____________, or range value. There are two methods that can be used to add and subtract rational numbers with

____________ denominators.

Some functions can be written as equations in two variables. The independent variable

represents the ____________ of a function. The dependent variable represents the

___________ of a function.

Examples: Finding Different Representations of a Function

Make a table and a graph of y = 3 - x2. Make a table of inputs and outputs. Use the table to make a graph.

Make a table and a graph of y = x + 1 Make a table of inputs and outputs. Use the table to make a graph.

Because a function has exactly ____________ output for each input, you can use the vertical

line test to test whether the graph is a function. If no vertical line intersects the graph at

more than one point, then the relation is a function. If any vertical line intersects the graph at

more than one point, then the relation is not a function.

Examples: Identifying Functions

Determine if the relationship represents a function.

Make an input-output table and use it to graph y = x3.

Make an input-output table and use it to graph y = x - 1.

Lesson 2-5

Equations, Tables and Graphs

Warm-Up

Examples: Using Equations to Generate Different Representations of Data

The height h of an airplane s seconds from take-off is h = 12s. Make a table and sketch a graph of the equation.

The height h of an helicopter s seconds from take-off is h = 15s. Make a table and sketch a graph of the equation.

Examples: Using Tables to Generate Different Representations of Data

Use a table to make a graph and to write an equation.

Examples: Using Graphs to Generate Different Representations of Data Use the graph to make a table and to write an equation.