Lesson 5.5.  “I know my graph is right!” exclaims Gloria. “I’ve checked and rechecked it. Yours must be wrong, Keith.”  Keith disagrees. “I’ve entered.

Slides:

Advertisements

Similar presentations

5.4 Correlation and Best-Fitting Lines

Advertisements

Carrying Out an Investigation in Science

Write an exponential function

Writing and Graphing Equations of Lines

Introduction The use of the coordinate plane can be helpful with many real-world applications. Scenarios can be translated into equations, equations can.

3.4 Graph of Linear Equations. Objective 1 Use the slope-intercept form of the equation of a line. Slide

EXAMPLE 1 Graph an equation of a circle Graph y 2 = – x Identify the radius of the circle. SOLUTION STEP 1 Rewrite the equation y 2 = – x

Introduction Tables and graphs can be represented by equations. Data represented in a table can either be analyzed as a pattern, like the data presented.

Find an Inverse Equation Algebraically. To find an inverse equation algebraically: 1.Switch the x and y in the equation. 2.Solve for y.

Power functions Functions of the form y = k * (x r ) where k is a non zero number and r is a positive integer are called power functions. Power functions.

 The graph of a function f is shown. Graph the inverse and describe the relationship between the function & its inverse. xy

DAY 7 – INVERSE OF A FUNCTION. 1.Use Exponential Regression to find an exponential function that contains the points (3, 54) and (4,162). 2.What is the.

Topic 2: Linear Equations and Regression

Lesson 5.3.  In this lesson you will investigate fractional and other rational exponents.  Keep in mind that all of the properties you learned in the.

Preview Warm Up California Standards Lesson Presentation.

FUNCTIONS AND GRAPHS.

Warm-up 1.Find f(12). 2.f(x)=140. Find x.. Answer 1.f(12) = 1 2. f(9) = 140.

Solving Systems by Graphing Lesson Is (4, 1) on the line y = 2x − 5? 2. Is (0, −5) on the line 4x + 2y = 10? 3. Is (−2, 7) on the line y = 3(x.

Goal: Find and use inverses of linear and nonlinear functions.

Lesson 12-2 Exponential & Logarithmic Functions

LESSON 2 – SOLVING LINEAR SYSTEMS GRAPHICALLY SYSTEMS OF LINEAR EQUATIONS.

Copyright © Cengage Learning. All rights reserved. Systems of Linear Equations and Inequalities in Two Variables 7.

Chapter 2 – Linear Equations and Functions

Unit 1: Scientific Process. Level 2 Can determine the coordinates of a given point on a graph. Can determine the independent and dependent variable when.

Solving Problems Given Functions Fitted to Data/Interpreting Slope and y-intercept Key Terms: Linear Fit Slope Scatter Plot 1 4.6: Solving Problems Given.

1.8 Inverse functions My domain is your range No! My range is your domain.

Chapter 5:Write the equation of a line Given Two Points.

A way to answer questions & solve problems How we understand the world around us A way or process used to investigate what is happening around you It provides.

Time (days)Distance (meters) The table shows the movement of a glacier over six days.

LESSON 7.4 Function Notation To learn function notation To evaluate functions by substitution, by using the graphs drawn by hand, and on the graphing calculator.

Copyright © 2009 Pearson Education, Inc. CHAPTER 1: Graphs, Functions, and Models 1.1 Introduction to Graphing 1.2 Functions and Graphs 1.3 Linear Functions,

Notes: Slope and Trend What is slope? How do you find the slope of a line?

Solving Systems of Equations by Graphing

Linear Equations and Their Graphs Chapter 6. Section 1: Rate of Change and Slope The dependent variable is the one that depends on what is plugged in.

Use function notation to evaluate and interpret functions

Lesson 1.6 Inverse Functions. Inverse Function, f -1 (x): Domain consists of the range of the original function Range consists of the domain of the original.

2.5 CORRELATION AND BEST-FITTING LINES. IN THIS LESSON YOU WILL : Use a scatter plot to identify the correlation shown by a set of data. Approximate the.

Section 1.4 Equations of Lines and Modeling Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Warm Ups! Find f(g(x)) and g(f(x)) for each of the following: 1.F(x)= 2x +1, g(x) = (x-1)/2 2.F(x) = ½ x + 3, g(x) = 2x-6.

WARM UP GRAPHING LINES Write the equation in slope- intercept form and then Graph. (Lesson 4.7) 1.3x + y = 1 2.x + y = 0 3.y = -4 3.

5.3 Write Linear Equations in Point-Slope Form Big Idea: -Verify that a point lies on a line, given an equation of a line. -Derive linear equations by.

Review after Christmas!. Solve the below equations for the variable..5 (6x +8) = 16 1.

Using Graphs and Tables to Solve Linear Systems 3-1

 I can… ◦ Find the inverse of a given relation or function.

Lesson 1.6 Page 69: #1-77 (EOO) EXTRA CREDIT: Pages (Do any 20 problems…You choose )

5.1 Solving Systems of Equations Objectives: --To identify a system of equations --To determine if a point is a solution to a system --To use graphing.

WARM UP WRITING EQUATIONS Write in slope-intercept form the equation of the line that passes through the given point and has the given slope. (Lesson 5.2)

Holt Algebra Linear, Quadratic, and Exponential Models Warm Up Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24).

Direct Variation 88 Warm Up Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. 1. y – 3 =

Semester 1 Final Review D Plot the point (4, -2) in the coordinate plane. (Lesson 4.1) Name the quadrant the point is in.

Unit 4 Part B Concept: Best fit Line EQ: How do we create a line of best fit to represent data? Vocabulary: R – correlation coefficient y = mx + b slope.

Algebra 2 Solving Systems Using Tables and Graphs Lesson 3-1.

OBJECTIVE I will use slope-intercept form to write an equation of a line.

Aim: How to plot or graph data

Building Linear Models from Data

5-Minute Check Lesson 3-4.

Day 3 – Graphs of Linear Equations

Day 3 – Graphs of Linear Equations

Day 76 – Review of Inverse Functions

Objectives Write equations and graph circles in the coordinate plane.

Choosing the Best Method

5.4 Finding Linear Equations

Graphing Skills for 2.1 Assessments

Day 7 – Inverse of a Function

Aim: How to plot or graph data

Chapter 4 Review.

Presentation transcript:

Lesson 5.5

 “I know my graph is right!” exclaims Gloria. “I’ve checked and rechecked it. Yours must be wrong, Keith.”  Keith disagrees. “I’ve entered these data into my calculator too, and I made sure I entered the correct numbers.”  Can you explain what is happening? Gloria and Keith are sharing their graphs for the same set of data.

 In this investigation you will use graphs, tables, and equations to explore the inverses of several functions.  Graph the equation f(x) =6+3x on your calculator. Complete the table for this function.

 Because the inverse is obtained by switching the independent and dependent variables, you can find five points on the inverse of function f by swapping the x- and y- coordinates in the table. Complete the table for the inverse.

 Graph the five points you found in the last by creating a scatter plot. Describe the graph and write an equation for it. Graph your equation and verify that it passes through the points in the table from the last step.

 Repeat the previous steps for each of these functions. You may need to write more than one equation to describe the inverse.

 Study the graphs of functions and their inverses that you made. What observations can you make about the graphs of a function and its inverse?  You create the inverse by switching the x- and y-values of the points. How can you apply this idea to find the equation of the inverse from the original function? Verify that your method works by using it to find the equations for the inverses of functions f, g, and h.

 A 589 mi flight from Washington, D.C., to Chicago took 118 min. A flight of 1452 mi from Washington, D.C., to Denver took 222 min. Model this relationship both as (time, distance) data and as (distance, time) data.  If a flight from Washington, D.C., to Seattle takes 323 min, what is the distance traveled?  If the distance between Washington, D.C., and Miami is 910 mi, how long will it take to fly from one of these two cities to the other?

 If you know the time traveled and want to find the distance, then time is the independent variable, and the points known are (118, 589) and (222, 1452).  The slope is or approximately 8.3 mi/min.  Using the first point to write an equation in point-slope form, you get To find the distance between Washington, D.C., and Seattle, substitute 323 for the time, t:

 If you know distance and want to find time, then distance is the independent variable. The two points then are (589, 118) and (1452, 222). This makes the slope  or approximately 0.12 min/mi. Using the first point again, the equation for time is

To find the time of a flight from Washington, D.C. to Miami, substitute 910 for the distance, d.

 You can also use the first equation for distance and solve for t to get the second equation, for time.

 Find the composition of this function with its inverse. f(x)=4-3x

 When you take the composition of a function and its inverse, you get x. How does the graph of y = x relate to the graphs of a function and its inverse? Look carefully at the graphs below to see the relationship between a function and its inverse.