Piecewise Functions.

Slides:

Advertisements

Similar presentations

Quadratic Functions By: Cristina V. & Jasmine V..

Advertisements

1. 2. Warm-Up Domain Range INQ:______________ INT:______________

Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

Graph 8 a. Graph b. Domain _________ c. Range __________

Graphing Piecewise Functions

Piecewise Functions and Step Functions

3.7 Graphing Rational Functions Obj: graph rational functions with asymptotes and holes and evaluate limits of rational functions.

Limit Laws Suppose that c is a constant and the limits lim f(x) and lim g(x) exist. Then x -> a Calculating Limits Using the Limit Laws.

Distance, Circles Eric Hoffman Calculus PLHS Aug

Functions and Graphs 1.2. FUNCTIONSFUNCTIONS Symmetric about the y axis Symmetric about the origin.

Pre-Calculus Section 1-3B Functions and Their Graphs.

Bellwork 1. Write the equation of a line that passes through (-2, 5) and is perpendicular to 4x – 3y = Write the equation of a line that passes.

Each element in A must be matched with an element in B Ex– (0,3) (3,2) (9,4) (12,5) Some elements in the range may not be matched with the domain. Two.

1.4 Functions I. Function A) Definition = a relation in which each value of x has exactly one solution y. B) Testing for functions. 1) From a graph: Use.

Bellwork: Graph each line: 1. 3x – y = 6 2. Y = -1/2 x + 3 Y = -2

Piecewise Graphs A piecewise function is defined by at least two equations, each of which applies to a different part of the function’s domain. One example.

Section 1.7 Piecewise Functions. Vocabulary Absolute Value Function – a piecewise function, written as f(x)=, where f(x) 0 for all values of x. Greatest.

Library of Functions You should be familiar with the shapes of these basic functions. We'll learn them in this section.

The Remainder and Factor Theorems

Section 4.3 Riemann Sums and Definite Integrals. To this point, anytime that we have used the integral symbol we have used it without any upper or lower.

Solving Equations Using Tables Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

-What is quadratic inequality -How to graph quadratic inequality 4-8 Quadratic Inequalities.

Lesson 1 Contents Example 1Graph a Quadratic Function Example 2Axis of Symmetry, y-Intercept, and Vertex Example 3Maximum or Minimum Value Example 4Find.

1.6 Step and Piecewise Functions. Objective To identify and graph step and piecewise- defined functions.

2.7 Piecewise Functions p In real life functions are represented by a combination of equations, each corresponding to a part of the domain. These.

Tell Me Everything You Can About The Graph Below.

Everyone needs a small white board, marker, and eraser rag 1.

PIECEWISE FUNCTIONS. PIECEWISE FUNCTION Objectives: 1.Understand and evaluate Piecewise Functions 2.Graph Piecewise Functions 3.Graph Step Functions Vocabulary:

2.2 day 3 The Piecewise Function

Warm-Up! Solve, graph and give the interval notation for:

Continuity Take out assignment from Tuesday. Continuous The graph of a piecewise function is said to be continuous if you can trace the graph with your.

PIECEWISE FUNCTIONS. What You Should Learn: ① I can graph any piecewise function. ① I can evaluate piecewise functions from multiple representations.

And a review of scientific notation 2.7 – Piecewice Functions.

2.5 Warm Up Graph, identify intercepts, zeros, and intervals of increase and decrease. Compare to parent function. y = 2 x

CHAPTER 1.7 Piecewise Functions.

Ch 4-3 Piecewise and Stepwise Functions C.N.Colon ALGEBRA-HP SBHS.

Warm Up Graph the following functions on the same coordinate plane:

2-2 Extension Part 2: Piecewise Functions

What piecewise function represents the graph?

Ch. 2 – Limits and Continuity

Warm Up Graph f(x) = 2x + 3 Graph f(x) = -3x + 1

Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.

The Remainder and Factor Theorems

Ch. 2 – Limits and Continuity

Piecewise Functions.

Warm Up State the domain and range of the following equations:

Polynomial Functions and Models

Evaluating Piecewise and Step Functions

Evaluating Piecewise Functions

Piecewise Functions At least 2 equations, each of which applies to a different part of the functions domain. It is like having 3 equations for 3 different.

Step functions Greatest integer functions Piecewise functions

A graphing calculator is required for some problems or parts of problems 2000.

Graphing and Evaluating The Piecewise Function A Series of Examples

Day 127 – Graphing Quadratics

23 – Limits and Continuity I – Day 1 No Calculator

Lesson 9 Absolute Value as Distance Graphing Special Functions

Topic/ Objective: To evaluate and graph piecewise and step functions.

Piecewise Graphs Lesson 7.4 Page 100.

Aim: What is the function notation?

AP Calculus AB/BC 1.2 Functions, p. 12.

Piecewise-Defined Function

Piecewise Functions.

Algebra 1 Section 12.9.

2.7 Piecewise Functions Algebra 2.

Piecewise-defined Functions

AP Calculus AB/BC 1.2 Functions.

20 – Understanding the Piecewise Function No Calculator

Factorise and solve the following:

Presentation transcript:

Piecewise Functions

Definition: Piecewise Function –a function defined by two or more functions over a specified domain.

f(x) = What do they look like? x2 + 1 , x  0 x – 1 , x  0 You can EVALUATE piecewise functions. You can GRAPH piecewise functions.

f(x) = Evaluating Piecewise Functions: Evaluating piecewise functions is just like evaluating functions that you are already familiar with. Let’s calculate f(2). f(x) = x2 + 1 , x  0 x – 1 , x  0 You are being asked to find y when x = 2. Since 2 is  0, you will only substitute into the second part of the function. f(2) = 2 – 1 = 1

f(x) = Let’s calculate f(-2). x2 + 1 , x  0 x – 1 , x  0 You are being asked to find y when x = -2. Since -2 is  0, you will only substitute into the first part of the function. f(-2) = (-2)2 + 1 = 5

f(x) = Your turn: 2x + 1, x  0 2x + 2, x  0 Evaluate the following: ? -3 f(5) = 12 ? f(1) = 4 ? f(0) = ? 2

f(x) = One more: 3x - 2, x  -2 -x , -2  x  1 x2 – 7x, x  1 Evaluate the following: f(-2) = ? 2 f(3) = -12 ? f(-4) = -14 ? ? f(1) = -6

 f(x) = Graphing Piecewise Functions: x2 + 1 , x  0 x – 1 , x  0 Determine the shapes of the graphs. Parabola and Line Determine the boundaries of each graph.     Graph the line where x is greater than or equal to zero. Graph the parabola where x is less than zero. 

  f(x) = Graphing Piecewise Functions: 3x + 2, x  -2 Determine the shapes of the graphs. Line, Line, Parabola Determine the boundaries of each graph.        