Determining function types from Data Tables

Slides:

Advertisements

Similar presentations

VISUALIZING DATA Ch. 2 Sect. 3. Graphing Data Charts are used to help analyze data Independent variable  Variable that is changed or manipulated  Experimenter.

Advertisements

Sequences. What is a sequence? A list of numbers in a certain order. What is a term? One of the numbers in the sequence.

9-7 Linear, Quadratic, and Exponential Models

EXAMPLE 1 Identify arithmetic sequences

Warm-up 1. Graph y = 3 x. ANSWER Tell whether the ordered pairs (0, 0), (1, 2), (2, 4), and (3, 6) represent a linear function. 2. For y = x 2 – 3x – 5,

EXAMPLE 3 Write an equation for a function

Linear vs Quadratic Graphs MAP4C. Degrees  Recall:  The degree of a polynomial is given by the highest power (exponent) in any term of the polynomial.

EXAMPLE 1 SOLUTION STEP 1 Graph a function of the form y = a x Graph the function y = 3 x and identify its domain and range. Compare the graph with the.

Linear, Exponential, and Quadratic Functions. Write an equation for the following sequences.

Grade 10 Mathematics Conjectures.

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.

How do scientists show the results of investigations?

I can find the slope of a line from a table or graph.

EXAMPLE 2 Graph an exponential function Graph the function y = 2 x. Identify its domain and range. SOLUTION STEP 1 Make a table by choosing a few values.

Arithmetic Sequences Standard: M8A3 e. Use tables to describe sequences recursively and with a formula in closed form.

Ch. 11 – Sequences & Series 11.1 – Sequences as Functions.

4 Linear Motion On a speed-versus-time graph the slope represents speed per time, or acceleration. 4.7 Graphs of Motion.

Homework Questions. Geometric Sequences In a geometric sequence, the ratio between consecutive terms is constant. This ratio is called the common ratio.

Homework Questions. Number Patterns Find the next two terms, state a rule to describe the pattern. 1. 1, 3, 5, 7, 9… 2. 16, 32, 64… 3. 50, 45, 40, 35…

COMMON CORE STANDARDS for MATHEMATICS FUNCTIONS: INTERPRETING FUNCTIONS (F-IF) F-IF3. Recognize that sequences are functions, sometimes defined recursively.

GRAPHING AND RELATIONSHIPS. GRAPHING AND VARIABLES Identifying Variables A variable is any factor that might affect the behavior of an experimental setup.

GraphsTablesEquationsVocabularyFunctions.

Comparing Functions and Identifying Linear and Non-linear Functions

Graphing Exponential Growth and Decay. An exponential function has the form b is a positive number other than 1. If b is greater than 1 Is called an exponential.

Geometric Sequences, Exponential Equations, Exponential Growth and Decay.

2.2 Square Root of a Function Square Root of the Linear Function

9-7 Linear, Quadratic, and Exponential Models. Linear, Quadratic, & Exponential Review.

Introduction to Graphing

Arithmetic and Geometric Means

Topics: Be able to writes equations of Linear Functions from numerical representations. Be able to writes equations of Absolute Value Functions from numerical.

Rules for Graphing.

Linear vs. Nonlinear Functions!

Straight Line Graphs (Linear Graphs)

10.8 Compare Linear, Exponential, and Quadratic Models

Position-Time and Velocity-Time Graphs

Sequences F.LE.1, 2, 5 F.BF.1, 2 A.SSE.1.a F.IF.1, 2, 3, 4

10.8 Compare Linear, Exponential, and Quadratic Models

Learning Target: I will graph a linear inequality.

2.2 Square Root of a Function Square Root of the Linear Function

1.7 - Geometric sequences and series, and their

Points of intersection of linear graphs an quadratic graphs

10.8 Compare Linear, Exponential, and Quadratic Models

Warm-up 1. Graph y = 3x. ANSWER

Module 1 Quiz Review.

8.6.4 Comparing Linear and Nonlinear Functions

Comparing and Contrasting Functions

Quadratic Functions and Models

Lesson 3: Linear Relations

Position-Time and Velocity-Time Graphs

Graph Exponential Functions

Compare Linear, Exponential, and Quadratic Models

10.8 Compare Linear, Exponential, and Quadratic Models

Linear Vs. Exponential Growth

Unit 6: Exponential Functions

Homework Questions.

Objectives Evaluate exponential functions.

Graphs Transformations.

Modelling Quadratic Functions

Warmup Solve cos 2

Solve each quadratic using whatever method you choose!

Velocity vs Time Graphs – Notebooks

First, identify the DOMAIN and RANGE for the relation below:

Remember, the coordinates should form a straight line.

Do Now 4/3/19 Take out HW from last night. Copy HW in your planner.

Arithmetic, geometric, or neither

Objectives Recognize and extend an arithmetic sequence.

Unit 13 Pretest.

Presentation transcript:

Determining function types from Data Tables MAP4C1

Linear We know linear graphs have a constant slope This means the graph increases by equal steps In a table of values, the 1st differences of the y-values are constant Linear

Quadratic graphs are curved and increase as a square of the x- values A plot of y vs x2, would yield a straight line In a table of values, the 2nd differences of the y-values are constant (the 1st differences make an arithmetic sequence). Quadratic

Exponentials Curved graphs, with varying bases Exists above the x-axis, unless it undergoes some sort of vertical translation The data table can be used here as well: the 1st differences of the y-values will yield a geometric sequence. The ratios of the 1st differences will be a constant Exponentials

Text work Page 442 #1, 2 Page 447 #1, 2 Page 463 #2,3, 6, 8 Page 470 Investigation – hand in! Text work