SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Standardized Test Practice SOLUTION Substitute several values of h into the equation C = h and solve for C.Then identify the table that.

Advertisements

SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner.

Substitute 3 for x and 4 for y. Simplify. Write original equation. Check whether each ordered pair is a solution of the equation. SOLUTION Which ordered.

EXAMPLE 5 Write and solve an equation

• Write an inequality that describes your goal in terms of x and y.

EXAMPLE 1 Using a Variable Expression Hot Air Balloons You are riding in a hot air balloon. After traveling 5 miles, the balloon speed changes to 6 miles.

EXAMPLE 1 Finding Intercepts Find the intercepts of the graph of y = 1 2 x – 5.5. STEP 1 To find the x -intercept, let y = 0 and solve for x. 1 2 = y x.

EXAMPLE 5 Solve a multi-step problem LIBRARY

EXAMPLE 6 Solve a multi-step problem Job Earnings You have two summer jobs at a youth center. You earn $8 per hour teaching basketball and $10 per hour.

EXAMPLE 3 Write an equation for a function

To write and graph an equation of a direct variation

Writing Function Rules

Warm-Up Write an equation in standard form of the line that passes through the given point and has the given slope m or that passes through the two given.

EXAMPLE 5 Solve a multi-step problem Recording Studio

EXAMPLE 4 Solve a multi-step problem CYCLING

Write and graph a direct variation equation

Functions. A function is a relation that has exactly one output for each input.

7.3 Introduction to Relations and Functions

Pg #4-12e, 13-18, 23, 24, 26, 36,

SOLUTION EXAMPLE 4 Graph an equation in two variables Graph the equation y = – 2x – 1. STEP 1 Construct a table of values. x–2–1 012 y31 –3–5.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Do Now 10/26/10 In your notebook, explain how you know a function is a function. Then answer if the following three tables are functions or not. x

3.2 Graph Linear Equations You will graph linear equations in a coordinate plane. Essential Question: How do you graph linear equations? You will learn.

Lesson 3.2 Graph Linear Equations Essential Question: How do you graph linear equations in the coordinate plane? Warm-up: Common Core CC.9-12.F.IF.7a.

4.4 Equations as Relations

Use the sign shown. A gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons)

Functions. What is a function? A function consists of: A function consists of: A set called the domain containing numbers called inputs, and a set called.

SOLUTION Write an inverse variation equation EXAMPLE 5 x–5–34824 y2.44–3–1.5–0.5 Tell whether the table represents inverse variation. If so, write the.

Read a problem and make a plan EXAMPLE 1 Running You run in a city where the short blocks on north-south streets are 0.1 mile long. The long blocks on.

Substitution Method: 1. Solve the following system of equations by substitution. Step 1 is already completed. Step 2:Substitute x+3 into 2 nd equation.

5-2 Direct Variation A direct variation is a relationship that can be represented by a function in the form y = kx, where k ≠ 0. The constant of variation.

Solving Linear Systems Using Linear Combinations There are two methods of solving a system of equations algebraically: Elimination (Linear Combinations)

Group C. How to Sketch the Graph of an Equation  Graph of Equation: The set of all solution points of an equation 1. Rewrite the equation so that one.

Warm-Up Exercises 1. Graph y = –x – 2 with domain –2, –1, 0, 1, and 2. ANSWER.

Warm Ups {(2,0) (-1,3) (2,4)} 1. Write as table 2. Write as graph 3. Write as map 4. State domain & range 5. State the inverse.

Use function notation to evaluate and interpret functions

12.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Model Inverse Variation.

EXAMPLE 3 Graph y = ab + k for 0 < b < 1 x – h Graph y = 3 –2. State the domain and range. 1 2 x+1 SOLUTION Begin by sketching the graph of y =, which.

Annie Tarwater Math If your car gets 20 miles to the gallon and you have 10 gallons of gas in your car how many miles will your car drive.

Lesson 4-6 Pages Functions and Linear Equations.

Graphing Lines by points Section 4.2 GRAB SOME GRAPH PAPER #26 I used to love mathematics for its own sake, and I still do, because it allows for no hypocrisy.

1.6 Represent Functions as Rules & Tables 1.  Function — a pairing where inputs are paired with only one output  Domain — the set of x values, or inputs.

Identify the domain and range of a function EXAMPLE 1 The input-output table shows the cost of various amounts of regular unleaded gas from the same pump.

1.7 Represent Functions as Rules and Tables Essential Question: How do you represent functions as rules and tables? Warm-up: 1. Write an expression:

Lesson 5: How to Interpret Relationships Between Variables.

Example 1 Read a problem and make a plan

1.6 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Represent Functions as Rules and Tables.

Warm-Up Exercises Warm-up: Countdown to Mastery Week #4 Homework- Page 44 #3-9 all #14-21 all.

Warm-Up Exercises Identify the domain and range of a function EXAMPLE 1 The input-output table shows the cost of various amounts of regular unleaded gas.

Chapter 7 Section 2. EXAMPLE 1 Graph y = b for 0 < b < 1 x Graph y = 1 2 x SOLUTION STEP 1 Make a table of values STEP 2 Plot the points from the table.

Warm-Up Exercises Lesson x – 2y = –8 2. –9x + 3y = 21 ANSWER y = 2x + 4 Rewrite the equation so y is a function of x. y = 3x + 7.

Do-Now Evaluate the expression when x = –3. –5 ANSWER 1. 3x

Section 3.6 Functions.

Function- A pairing of inputs with outputs such that each input is paired with exactly one output. (the inputs can’t repeat) Domain- inputs or x values.

Distinguish between independent and dependent variables.

Tables and Relations Review

Solve a system of linear equation in two variables

Lesson 4.2 Graph Linear Equations

Tables and Relations Review

The domain is the set of inputs: 10, 12, 13,

Basics of Functions and Their Graphs

Tables and Relations Review

Objectives Identify solutions of linear equations in two variables.

Domain and Range.

Tables and Relations Review

Make a table and a graph of the function y = 2x + 4

Graphing Linear Equations

Distinguish between independent and dependent variables.

Presentation transcript:

SOLUTION RUNNING The distance d (in miles) that a runner travels is given by the function d = 6t where t is the time (in hours) spent running. The runner plans to go for a 1.5 hour run. Graph the function and identify its domain and range. STEP 1 Identify whether the problem specifies the domain or the range. You know the amount of time the runner plans to spend running. Because time is the independent variable, the domain is specified in this problem. The domain of the function is 0 ≤ t ≤ 1.5. Solve a multi-step problem EXAMPLE 5

Solve a multi-step problem STEP 2 Graph the function. Make a table of values. Then plot and connect the points. t ( hours ) d ( miles ) 0369 STEP 3 Identify the unspecified domain or range. From the table or graph, you can see that the range of the function is 0 ≤ d ≤ 9.

SOLUTION EXAMPLE 6 Solve a related problem WHAT IF? Suppose the runner in Example 5 instead plans to run 12 miles. Graph the function and identify its domain and range. STEP 1 Identify whether the problem specifies the domain or the range. You are given the distance that the runner plans to travel. Because distance is the dependent variable, the range is specified in this problem. The range of the function is 0 ≤ d ≤ 12.

EXAMPLE 6 Solve a related problem STEP 2 Graph the function. To make a table, you can substitute d -values ( be sure to include 0 and 12) into the function d = 6t and solve for t. t ( hours ) 012 d ( miles ) 0612 STEP 3 Identify the unspecified domain or range. From the table or graph, you can see that the domain of the function is 0 ≤ t ≤ 2.

GUIDED PRACTICE for Examples 5 and 6 GAS COSTS For gas that costs $2 per gallon, the equation C = 2g gives the cost C (in dollars) of pumping g gallons of gas. You plan to pump $10 worth of gas. Graph the function and identify its domain and range. domain: 0 ≤ g ≤ 5, range: 0 ≤ C ≤ ANSWER