Objective: Identify even or odd functions. Warm up a.Describe where is the function increasing, decreasing or constant. b.What is the relative maximum?

Slides:

Advertisements

Similar presentations

WARM UP Zeros: Domain: Range: Relative Maximum: Relative Minimum:

Advertisements

Calculus Lesson 1.1 Part 3 of 3. Sketch the graph of the absolute value function:

Properties of Functions Section 1.6. Even functions f(-x) = f(x) Graph is symmetric with respect to the y-axis.

Obtaining Information from Graphs

Graphs of Functions Lesson 3.

Symmetry of Functions Even, Odd, or Neither?. Even Functions All exponents are even. May contain a constant. f(x) = f(-x) Symmetric about the y-axis.

Tuesday Evaluate these two functions Function Characteristics Even vs Odd Symmetry Concavity Extreme.

Lesson 1.3 Read: Pages Page 38: #1-49 (EOO), #61-85 (EOO)

1.5 – Analyzing Graphs of Functions

Domain Symmetry Function Operations Misc.Inverses.

Symmetry and Coordinate Graphs Symmetry and Coordinate Graphs Section 3-1 How do we determine symmetry using algebra? How do we classify functions as even.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 3.3 Properties of Functions.

Section 2.3 Properties of Functions. For an even function, for every point (x, y) on the graph, the point (-x, y) is also on the graph.

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

Sullivan PreCalculus Section 2.3 Properties of Functions Objectives Determine Even and Odd Functions from a Graph Identify Even and Odd Functions from.

Sullivan Algebra and Trigonometry: Section 3.2 Objectives Find the Average Rate of Change of Function Use a Graph to Determine Where a Function Is Increasing,

Section 1.3 – More on Functions. On the interval [-10, -5]: The maximum value is 9. The minimum value is – and –6 are zeroes of the function.

Objectives: Graph the functions listed in the Library of Functions

Chapter 3 Non-Linear Functions and Applications Section 3.1

3-1 Symmetry and Coordinate Graphs Pre Calc A. Point Symmetry Symmetric about the origin: any point in Quadrant I has a point in Quadrant III (rotate.

3.5-3 Symmetry, Monotonicity. In some cases, we will have some kind of symmetry in regards to graphs of a function – Symmetry = a specific part or portion.

3-1 Symmetry & Coordinate Graphs Objective: 1. To determine symmetry of a graph using algebraic tests. 2. To determine if a function is even or odd.

3-1 Symmetry and Coordinate Graphs. Graphs with Symmetry.

More on Functions and Their Graphs

SYMMETRY, EVEN AND ODD FUNCTIONS NOTES: 9/11. SYMMETRY, EVEN AND ODD FUNCTIONS A graph is symmetric if it can be reflected over a line and remain unchanged.

Chapter 1 Functions and Their Graphs

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.

Last Night’s HW  6. no  8. yes  32a. 2  32b. 5  32c. √x+2  33a. -1/9  33b. undefined  33c. 1/(y^2 + 6y) 66. D: (- ∞, 0) U (0, 2) U (2, ∞) 68. D:

Domain/Range/ Function Worksheet Warm Up Functions.

END BEHAVIOR & SYMMETRY Objective: describe the end behavior of a function; determine whether a function is “even, odd, or neither” How do the exponents.

Functions (but not trig functions!)

3.2 Properties of Functions. If c is in the domain of a function y=f(x), the average rate of change of f from c to x is defined as This expression is.

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.

Increasing & Decreasing Functions A function f is increasing on an interval if, for any x 1 and x 2, in the interval, x 1 < x 2 implies f(x 1 ) < f(x 2.

Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.

College Algebra 2.4 Properties of Functions Objectives: 1. Determine even or odd functions 2. Determine behavior of a function. 3. Find local min and max.

Equal distance from origin.

Symmetry and Asymptotes. f(-x) = f(x)EvenSymmetrical wrt y-axis f(-x) = -f(x)OddSymmetrical wrt origin Even Neither Odd Even Odd.

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

1. Use the graph to determine intervals where the function is increasing, decreasing, and constant.

AIM: What is symmetry? What are even and odd functions? Do Now : Find the x and y intercepts 1)y = x² + 3x 2) x = y² - 4 (3x + 1)² HW #3 – page 9 (#11-17,

Warm-Up. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

College Algebra Chapter 2 Functions and Graphs Section 2.7 Analyzing Graphs of Functions and Piecewise- Defined Functions.

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

Objective: Test for symmetry in polar equations.

Properties of Functions

Or ODD EVEN Functions.

3.1 Symmetry and Coordinate Graphs

Properties of Functions

Sullivan College Algebra: Section 3.3 Properties of Functions

Attributes of functions in their graph

Even and Odd Functions The easiest thing to do is to plug in 1 and -1 (or 2 and -2) if you get the same y, then it’s Even. If you get the opposite y, then.

4.3 Symmetry Which graph is NOT a function?

Warm-up: Determine which of the following are functions. A. B.

More on Functions and Their Graphs

Section 2.3 – Analyzing Graphs of Functions

Properties of Functions

Section 4.4 – Analyzing Graphs of Functions

Properties of Functions

Worksheet KEY 1) {0, 2} 2) {–1/2} 3) No 4) Yes 5) 6) 7) k = 1 8)

Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.

Functions: Even/Odd/Neither

Power Functions Investigating symmetry to determine if a power function is even, odd, or neither.

Chapter 2 More on Functions.

Properties of Functions

2.3 Properties of Functions

Properties of Functions

Properties of Functions

Properties of Functions

Presentation transcript:

Objective: Identify even or odd functions. Warm up a.Describe where is the function increasing, decreasing or constant. b.What is the relative maximum? c.What is the relative minimum?

1. 2. Pg 175 # 40,42,44,46,48,49,52,95,96,97

Example 1 Classify each function as symmetric w.r.t. y-axis, origin or neither.

Even Functions

Odd Functions

Identifying even or odd functions Graphically (look for symmetry) symmetric w.r.t y-axis: even symmetric w.r.t origin (rotational symmetry): odd Algebraically If F(- x) = F(x), then is even. If F(- x) = - F(x), then is odd. Example 2 Graph the function. Find the symmetry and decide if the function is even or odd. Confirm algebraically. a. b. c.

Assignment Pg 173 #17-32