Types of Functions, Rates of Change Lesson 1.4. Constant Functions Consider the table of ordered pairs The dependent variable is the same It is constant.

Slides:

Advertisements

Similar presentations

1 What Makes a Function Linear Lesson What Is A Line? Check out this list of definitions or explanations to the question  Define Line Define Line.

Advertisements

Polynomial Functions and Models Lesson 4.2. Review General polynomial formula a 0, a 1, …,a n are constant coefficients n is the degree of the polynomial.

Graphing Linear Equations In Slope-Intercept Form.

Formulas for Linear Functions Lesson What Do You Know about These Forms of Linear Equations? Standard form Slope Intercept form Slope-Point form.

Bell Quiz. Objectives Learn to write equations in slope-intercept form.

Functions and Equations of Two Variables Lesson 6.1.

Concavity and Rates of Change Lesson 2.5. Changing Rate of Change Note that the rate of change of the curve of the top of the gate is changing Consider.

Equations of Lines Lesson Point Slope Form We seek the equation, given point and slope Recall equation for calculating slope, given two points.

Systems of Linear Equations Recalling Prior Knowledge.

Linear Functions and Models Lesson 2.1. Problems with Data Real data recorded Experiment results Periodic transactions Problems Data not always recorded.

Chapter 3 – Linear Systems

Quadratic Functions and Models Lesson 3.1. Nonlinear Data When the points of the function are plotted, they do not lie in a straight line. This graph.

4.2 Graphing linear equations Objective: Graph a linear equation using a table of values.

Lesson 13 Graphing linear equations. Graphing equations in 2 variables 1) Construct a table of values. Choose a reasonable value for x and solve the.

Geometric Properties of Linear Functions Lesson 1.5.

Graphing Linear Equations

Thursday Section 3-1: Graphing Systems of Equations Pages in textbook.

Warm Up #10 1.) Graph 5x + 7y =35 2.) Graph y= 2x -3.

Warm Up 1. Find the x- and y-intercepts of 2x – 5y = 20.

Visualization of Data Lesson 1.2. One-Variable Data Data in the form of a list Example, a list of test scores {78, 85, 93, 67, 51, 98, 88} Possible to.

Check it out! : Interpreting Parameters. You are buying a membership to a gaming store. The membership fee is $5 per month and each game costs.

Relations and Functions

2.3 – Functions and Relations

 1.  2..27v-1.6=.32v-2. Slope-Intercept Form y = mx + b m = slope b = y-intercept Slope-Intercept Form y = mx + b m = slope b = y-intercept.

Algebra Using Graphs & Tables to Solve Linear Systems

Polar Coordinates Lesson Points on a Plane Rectangular coordinate system  Represent a point by two distances from the origin  Horizontal dist,

Lesson 1-3, 1-4 Represent Functions as Graphs; Graphing Linear Equations using Intercepts.

LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You.

Points and Ordered Pairs Plot points on the rectangular coordinate system. Plot the x coordinate first then the y coordinate. This is an ordered pair.

Practice 1.) Solve for y : 4x + 2y = -8 2.) Solve for y: 3x – 5y = 10 3.) Graph the equation: 3x – 2y = 5 x y O

Graphs of Sine and Cosine Functions Lesson Ordered Pairs  Consider the values for x and y in the table to the right  Note Period = 2 π Maximum.

Functions, Equations, and Graphs Ch. 2.3 Linear Functions and Slope-Intercept Form EQ: How can I graph linear functions? I will graph linear functions.

Linear, Quadratic, and Exponential Models 11-4

Rates of Change Lesson Which Is Best?  Which roller coaster would you rather ride?  Why? Today we will look at a mathematical explanation for.

Graphing Linear Equations From the beginning. What is a Linear Equation? A linear equation is an equation whose graph is a LINE. Linear Not Linear.

Objectives Identify linear functions and linear equations.

1 Basic Differentiation Rules Lesson 3.2A. 2 Basic Derivatives Constant function – Given f(x) = k Then f’(x) = 0 Power Function –Given f(x) = x n Then.

Lines in the Coordinate Plane

Holt Algebra Identifying Linear Functions 5-1 Identifying Linear Functions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation.

Presentation Index Graphing Equations of Lines QUIZ: Graphing Equations of Lines.

Copyright © 2015, 2008, 2011 Pearson Education, Inc. Section 1.4, Slide 1 Chapter 1 Linear Equations and Linear Functions.

4-1 Identifying Linear Functions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Algebra 1.

Using Graphs and Tables to Solve Linear Systems 3-1

Holt McDougal Algebra Identifying Linear Functions Identify linear functions and linear equations. Graph linear functions that represent real- world.

Graphing Linear Equations 4.2 Objective 1 – Graph a linear equation using a table or a list of values Objective 2 – Graph horizontal or vertical lines.

7.3 Linear Equations and Their Graphs Objective: To graph linear equations using the x and y intercepts To graph horizontal and vertical lines.

Linear Graphs and Modelling Plotting straight line graphs Plotting linear graphs on the calculator Finding gradients of straight lines Equations of straight.

TODAY IN ALGEBRA…  Warm Up: Writing equation in slope- intercept form, then identifying the slope and y-intercept  Learning Goal: 4.6 You will write.

What happens if we graph a system of equations and the lines intersect? y = x-1 y = 2x-2.

Parametric Equations Lesson Movement of an Object Consider the position of an object as a function of time  The x coordinate is a function of.

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).

1 The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight.

Warm Up 1. Find the slope and y-intercept of the line that passes through (4, 20) and (20, 24). The population of a town is decreasing at a rate of 1.8%

Lesson 4-1 Solving linear system of equations by graphing

Graphing Linear Equations

7.1 Solving Systems of Equations by Graphing

What Makes a Function Linear

Types of Functions, Rates of Change

Polynomial Functions and Models

Slopes and Equations of Lines

Quadratic Functions and Models

The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight.

Rates of Change Lesson 1.2.

Formulas for Linear Functions

Lesson Objectives: I will be able to …

Differentiating between relations and functions

Warm up 21 1.) Determine the slope and y intercept of the line y=7x ) Determine the slope and the yintercept of the line 7x- 4y=3 3.) Graph y=1/2.

Concavity and Rates of Change

Equations With Two Variables pages

Lesson 4.1: Identifying linear functions

Presentation transcript:

Types of Functions, Rates of Change Lesson 1.4

Constant Functions Consider the table of ordered pairs The dependent variable is the same It is constant The graph is a horizontal line Month Rent Paid$735

Linear Function Can be represented by Where a and b are constants See Geogebra exampleexample

Slope and Y-Intercept Considering y = m * x + b The b is the y-intercept Where on the y-axis, the line intersects On your calculator Go to Y= screen Enter at Y1 (2/3) * x + 5 Predict what the graph will look like before you specify F2, 6 for standard zoom

Family of Linear Functions Slope = Rate of Change y=3x + 5 Slope = m = 3 y-intercept = b = 5

Slope and Y-Intercept The function y = (2/3) * x + 5 Slope = 2/3 (up to the right) Y-intercept = 5

Linear Functions Consider this set of ordered pairs If we plot the points and join them we see they lie in a line xy

Rate of Change Given function y = 3x + 5 xy

Rate of Change Try calculating for different pairs of (x, y) points You should discover that the rate of change is constant … in this case, 3 xy Geogebra Demo

Slope When slope = Try y = -7x – 3 (predict the results before you graph)

Family of Linear Functions Calculating slope with two ordered pairs (X 1, Y 1 ) (X 2, Y 2 ) Given two ordered pairs, (7,5) and (-3,12). What is the slope of the line through these two points?

Rate of Change Consider the function Enter into Y= screen of calculator View tables on calculator (♦ Y) You may need to specify the beginning x value and the increment

Rate of Change As before, determine the rate of change for different sets of ordered pairs xsqrt(x)

Rate of Change (NOT a constant) You should find that the rate of change is changing – NOT a constant. Contrast to the first function y = 3x + 5 Geogebra Demo

Function Defined by a Table Consider the two functions defined by the table The independent variable is the year. Predict whether or not the rate of change is constant Determine the average rate of change for various pairs of (year, sales) values Year CD sales LP sales

Warning Not all functions which appear linear will actually be linear!! Consider the set of ordered pairs Graph them Decide whether graph is linear Check slope for different pairs tP

Results Graph appears straight But … rate of change is not a constant tPslope

Assignment Lesson 1.4 Page 53 Exercises 1 – 65 EOO