Splash Screen. Then/Now You identified and graphed linear, exponential, and quadratic functions. Identify and graph step functions. Identify and graph.

Slides:

Advertisements

Similar presentations

Splash Screen Inequalities Involving Absolute Values Lesson5-5.

Advertisements

Splash Screen Graphing Equations in Slope-intercept Form Lesson 4-1.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–4) Then/Now Example 1:Expressions with Absolute Value Key Concept: Absolute Value Equations.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–2) CCSS Then/Now New Vocabulary Key Concept: Feasible Regions Example 1: Bounded Region Example.

Splash Screen. Then/Now You solved systems of linear inequalities by graphing. Find the maximum and minimum values of a function over a region. Solve.

Over Lesson 1–3 A.A B.B C.C D.D 5-Minute Check 1 A.Multiplicative Identity B.Additive Identity C.Associative Property of Addition D.Associative Property.

Piecewise Functions and Step Functions

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 5–4) CCSS Then/Now New Vocabulary Key Concept: Sum and Difference of Cubes Example 1:Sum and.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 9–6) CCSS Then/Now New Vocabulary Key Concept: Greatest Integer Function Example 1:Greatest.

Splash Screen. Lesson Menu Five-Minute Check Then/Now New Vocabulary Key Concept: Real Numbers Example 1:Use Set-Builder Notation Example 2:Use Interval.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–5) CCSS Then/Now New Vocabulary Example 1:Piecewise-Defined Function Example 2:Write a Piecewise-Defined.

Graphing Quadratic Functions

Chapter 2 Section 6. Psychology One psychologist charges for counseling sessions at the rate of $85 per hour or any fraction thereof. Draw a graph that.

2.6 Notes: Special Functions

Then/Now Identify and graph step functions. Identify and graph absolute value and piecewise-defined functions.

Splash Screen. Lesson Menu Five-Minute Check (over Chapter 3) CCSS Then/Now New Vocabulary Example 1:Graph a Quadratic Function by Using a Table Key Concept:

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–3) Then/Now New Vocabulary Example 1: Solve a Logarithmic Equation Key Concept: Property of.

Over Lesson 9–1 A.A B.B C.C D.D 5-Minute Check 1 A.D = {all real numbers}, R = {y | y ≤ –2} B.D = {all real numbers}, R = {y | y ≥ –2} C.D = {all real.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–1) CCSS Then/Now New Vocabulary Key Concept: Linear Function Example 1: Solve an Equation.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–7) CCSS Then/Now New Vocabulary Example 1:Dashed Boundary Example 2:Real-World Example: Solid.

Graphing Quadratic Functions Lesson 9-1 Splash Screen.

Special Functions Lesson 9-7 Splash Screen LEARNING GOAL Understand how to identify and graph step functions, absolute value functions and piecewise-defined.

Splash Screen. Concept Example 1 Limitations on Domain Factor the denominator of the expression. Determine the values of x for which is not defined.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 1–4) Then/Now New Vocabulary Example 1:Use a Replacement Set Example 2:Standardized Test Example.

Splash Screen. Lesson Menu Five-Minute Check Then/Now New Vocabulary Key Concept: Real Numbers Example 1:Use Set-Builder Notation Example 2:Use Interval.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–7) CCSS Then/Now New Vocabulary Example 1:Dashed Boundary Example 2:Real-World Example: Solid.

Special Functions Constant Function ex. y = 4.95 The Charlie’s Smorgasbord Function Absolute Value Function ex. y = | x | absolute V alue Step (Greatest.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 2–5) Then/Now New Vocabulary Example 1:Piecewise-Defined Function Example 2:Write a Piecewise-Defined.

Splash Screen. Lesson Menu Five-Minute Check Then/Now New Vocabulary Key Concept: Linear and Polynomial Parent Functions Key Concept: Square Root and.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–1) CCSS Then/Now New Vocabulary Key Concept: Linear Function Example 1: Solve an Equation.

CCSS Content Standards F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of.

Splash Screen. Then/Now You represented relations as tables, graphs, and mappings. Find the inverse of a relation. Find the inverse of a linear function.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 1–3) Then/Now New Vocabulary Key Concept: Absolute Value Example 1:Evaluate an Expression with.

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.

Splash Screen. Then/Now You identified and graphed linear, exponential, and quadratic functions. Identify and graph step functions. Identify and graph.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 3–2) CCSS Then/Now New Vocabulary Key Concept: Feasible Regions Example 1: Bounded Region Example.

Splash Screen. Over Lesson 1–6 5-Minute Check 1 Which expresses the relation {(–1, 0), (2, –4), (–3, 1), (4, –3)} correctly? A.B. C.

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–3) CCSS Then/Now New Vocabulary Key Concept: Vertical and Horizontal Asymptotes Example 1:Graph.

Splash Screen. Over Lesson 11–1 5-Minute Check 1.

Intro. Unit 4-1: Graphing Quadratic Functions Then/Now You identified and manipulated graphs of functions. Graph quadratic functions. Find and interpret.

Splash Screen Unit 6 Exponents and Radicals. Splash Screen Essential Question: How do you evaluate expressions involving rational exponents?

Special Functions: Step, Absolute Value, and Piecewise Functions.

2.6: Special Functions Algebra 2.

LESSON 2–6 Special Functions.

Name:__________ warm-up 9-7

piecewise-defined function

Solve the system of inequalities by graphing. x ≤ 2 y > 3

Solving Logarithmic Equations and Inequalities

Presentation transcript:

Splash Screen

Then/Now You identified and graphed linear, exponential, and quadratic functions. Identify and graph step functions. Identify and graph absolute value and piecewise-defined functions.

Vocabulary step function piecewise-linear function greatest integer function absolute value function piecewise-defined function

Concept

Example 1 Greatest Integer Function First, make a table of values. Select a few values between integers. On the graph, dots represent points that are included. Circles represent points that are not included. Answer: Because the dots and circles overlap, the domain is all real numbers. The range is all integers.

Example 1 A.D = all real numbers, R = all real numbers B.D = all integers, R = all integers C.D = all real numbers, R = all integers D.D = all integers, R = all real numbers

Example 2 Step Function TAXI A taxi company charges a fee for waiting at a rate of $0.75 per minute or any fraction thereof. Draw a graph that represents this situation. The total cost for the fee will be a multiple of $0.75, and the graph will be a step function. If the time is greater than 0 but less than or equal to 1 minute, the fee will be $0.75. If the time is greater than 2 minutes but less than or equal to 3 minutes, you will be charged for 3 minutes, or $2.25.

Example 2 Step Function Answer:

Example 2 SHOPPING An on-line catalog company charges for shipping based upon the weight of the item being shipped. The company charges $4.75 for each pound or any fraction thereof. Draw a graph of this situation.

Example 2 A.B. C.

Concept

Example 3 Absolute Value Function Graph f(x) = │2x + 2│. State the domain and range. Since f(x) cannot be negative, the minimum point of the graph is where f(x) = 0. f(x) = │2x + 2│Original function 0 = 2x + 2Replace f(x) with 0. –2 = 2xSubtract 2 from each side. –1 = xDivide each side by 2.

Example 3 Absolute Value Function Next, make a table of values. Include values for x > –5 and x < 3. Answer: The domain is all real numbers. The range is all nonnegative numbers.

Example 3 A.D = all real numbers, R = all numbers ≥ 0 B.D = all numbers ≥ 0 R = all real numbers, C.D = all numbers ≥ 0, R = all numbers ≥ 0 D.D = all real numbers, R = all real numbers Graph f(x) = │x + 3│. State the domain and range.

Example 4 Piecewise-Defined Function Graph the first expression. Create a table of values for when x < 0, f(x) = –x, and draw the graph. Since x is not equal to 0, place a circle at (0, 0). Next, graph the second expression. Create a table of values for when x ≥ 0, f(x) = –x + 2, and draw the graph. Since x is equal to 0, place a dot at (0, 2).

Example 4 Piecewise-Defined Function Answer: D = all real numbers, R = all real numbers

Example 4 A.D = y│y ≤ –2, y > 2, R = all real numbers B.D = all real numbers, R = y│y ≤ –2, y > 2 C.D = all real numbers, R = y│y < –2, y ≥ 2 D.D = all real numbers, R = y│y ≤ 2, y > –2

Concept

End of the Lesson