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Calculus Lesson 1.1 Part 3 of 3
Sketch the graph of the absolute value function:
Sketch the graph of the Greatest Integer Function: (also known as the stair step function)
If a function f satisfies the rule f(-x) = f(x) for every member of x in its domain, then f is called an even function. (Figure 19)
The geometric significance is that an even function is symmetric with respect to the y-axis.
If f satisfies f(-x) = -f(x), then f is called an odd function. (Figure 20)
If f satisfies f(-x) = -f(x), then f is called an odd function. (Figure 20) The graph of an odd function is symmetric about the origin.
Determine whether each of the following functions is even, odd, or neither.
The graph in figure 22 rises from A to B, falls from B to C, and rises again from C to D. The function f is said to be increasing on the interval [a,b], decreases from [b,c], and increases again from [c,d].
Assignment: Pg. 22 #41, 43, 44, 49, 50, 51, 57, 61, 65, 67
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.
Title of Lesson: Graphs of Functions Section 1.3 Pages in Text Any Relevant Graphics or Videos.
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.
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.
Graphs of Functions Lesson 3. Warm Up – Perform the Operations and Simplify.
Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Section 3.3 Properties of Functions.
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.
Section 2.4 Symmetry Copyright ©2013, 2009, 2006, 2001 Pearson Education, Inc.
Sullivan PreCalculus Section 2.3 Properties of Functions Objectives Determine Even and Odd Functions from a Graph Identify Even and Odd Functions from.
LIBRARY OF FUNCTIONS Objectives: Graph the functions listed in the Library of Functions.
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 3.5C: Graphs of Functions Sketch Piecewise-Defined Functions:
FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.
Properties of Functions Section 1.6. Even functions f(-x) = f(x) Graph is symmetric with respect to the y-axis.
Copyright © Cengage Learning. All rights reserved. Pre-Calculus Honors 1.3: Graphs of Functions HW: p.37 (8, 12, 14, all, even, even)
Chapter 2 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.
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 ollege A lgebra Functions and Graphs (Chapter1) 1.
Copyright © Cengage Learning. All rights reserved. 1 Functions and Their Graphs.
Section 1.2 Analyzing Graphs x is the distance from the y-axis f(x) is the distance from the x-axis p. 79 Figure 1.6 (open dot means the graph does not.
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:
Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc More on Functions and Their Graphs.
Polynomials Graphing and Solving. Standards MM3A1. Students will analyze graphs of polynomial functions of higher degree. a. Graph simple polynomial functions.
Copyright © 2011 Pearson Education, Inc. Slide Graphs of Basic Functions and Relations Continuity (Informal Definition) A function is continuous.
Graph of Logarithmic functions. 1 b 1 b 2 2 Graph of y = log b x b >1 If x = , then y = /b b 1 b /b.
1.2: Functions and Graphs. Relation- for each x value, there can be any y-values. Doesn’t pass the VLT. (ex. (1,2), (2,4), (1,-3) Function- For each x-value,
END BEHAVIOR & SYMMETRY Objective: describe the end behavior of a function; determine whether a function is “even, odd, or neither” How do the exponents.
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.
Parent Graphs. Square(Quadratic) Function f(x) = x2 Domain: all real number Range: all nonnegative real number Has intercept of (0,0) Decreases on interval.
1.5 Analyzing Graphs of Functions (-1,-5) (2,4) (4,0) Find: a.the domain b.the range c.f(-1) = d.f(2) = [-1,4) [-5,4] -5 4.
3-1 Symmetry and Coordinate Graphs. Graphs with Symmetry.
A Library of Parent Functions Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 Definition: Functions Linear Function.
FUNCTIONS AND MODELS 1. The fundamental concepts that we deal with in calculus are functions. This chapter prepares the way for calculus by discussing:
1.5 – Analyzing Graphs of Functions What you should learn: Use the vertical line test for functions. Find the zeros of functions Determine intervals on.
Functions and Their Graphs. 2 Identify and graph linear and squaring functions. Recognize EVEN and ODD functions Identify and graph cubic, square root,
Lesson 2.6 Read: Pages Page 152: #1-37 (EOO), 47, 49, 51.
EVEN and ODD FUNCTIONS ADV145 EVEN FUNCTION: when the “directed distance” from the x-axis to the graph of the function is equal to the right and left of.
Copyright © 2007 Pearson Education, Inc. Slide 2-1.
Domain – all of the x-coordinates of a graph Range – all of the y-coordinates of a graph Notation ◦ Interval notation ◦ Set Notation Proper use.
Increasing and Decreasing Functions Relative Maxima and Relative Minima Even and Odd Functions and Symmetry Functions and Difference Quotients.
Chapter 1 Functions and Their Graphs Even and Odd Functions Objectives: Identify and graph step functions and other piecewise-defined functions.
October 14, 2011 At the end of today, you will be able to Identify and graph step, constant, identity functions, piecewise functions, and absolute value.
Curve Sketching 2.7 Geometrical Application of Calculus a) Find stationary points. (f’(x)=0) b) Find points of inflection. (f”(x)=0) c) Find intercepts.
Copyright © Cengage Learning. All rights reserved. 1 Functions and Limits.
College Algebra Chapter 2 Functions and Graphs Section 2.7 Analyzing Graphs of Functions and Piecewise- Defined Functions.
Pre-Calculus Lesson 3: Translations of Function Graphs Vertical and horizontal shifts in graphs of various functions.
A Library of Parent Functions MATH Precalculus S. Rook.
Analyzing Graphs of Functions MATH Precalculus S. Rook.
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