Lesson 4.5. The graph of the square root function,, is another parent function that you can use to illustrate transformations. From the graphs below,

Slides:

Advertisements

Similar presentations

5/2/ Parent Functions1 warm_up #5 How do you think you did on the last test? What parts did you do well in? What parts could you have improved upon?

Advertisements

Function Families Lesson 1-5.

Unit 3 Functions (Linear and Exponentials)

Unit 3 Functions (Linear and Exponentials)

Essential Question: In the equation f(x) = a(x-h) + k what do each of the letters do to the graph?

Quadratic Functions Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function attributes:

8.3 Notes Handout.

Warm-Up: you should be able to answer the following without the use of a calculator 2) Graph the following function and state the domain, range and axis.

To introduce the general form of a quadratic equation To write quadratic equations that model real-world data To approximate the x-intercepts and other.

6.5 - Graphing Square Root and Cube Root

Radical Functions 8-7 Warm Up Lesson Presentation Lesson Quiz

Warm Up Identify the domain and range of each function.

 1. x = x = 11/15 3. x = x = x ≤ 7 6. x > x ≥ 3/2 8. x ≤ hours or more 10. x = x = 27/ x =

Unit 5 – Linear Functions

Objective: Students will be able to graph and transform radical functions.

Parent Functions General Forms Transforming linear and quadratic function.

Homework: p , 17-25, 45-47, 67-73, all odd!

Parent Functions and Transformations. Parent Graphs In the previous lesson you discussed the following functions: Linear Quadratic Cubic, Square root.

2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.

Graph Absolute Value Functions using Transformations

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,

Advanced Algebra II Notes 4.5 Reflections and the Square Root Family

4-1 Quadratic Functions Unit Objectives: Solve a quadratic equation. Graph/Transform quadratic functions with/without a calculator Identify function.

Transformations of functions

Jeopardy Final Jeopardy Parent Functions Equations Stats Other $100

P. 82. We will find that the “shifting technique” applies to ALL functions. If the addition or subtraction occurs prior to the function occurring, then.

Graphing Absolute Value Functions using Transformations.

Graphs & Models (Precalculus Review 1) September 8th, 2015.

3.4 Graphs and Transformations

TRANSFORMATION OF FUNCTIONS FUNCTIONS. REMEMBER Identify the functions of the graphs below: f(x) = x f(x) = x 2 f(x) = |x|f(x) = Quadratic Absolute Value.

Math-3 Lesson 1-3 Quadratic, Absolute Value and Square Root Functions

Objectives Vertical Shifts Up and Down

Square Root Function Graphs Do You remember the parent function? D: [0, ∞) R: [0, ∞) What causes the square root graph to transform? a > 1 stretches vertically,

Parent Graphs and Transformations

Warm Up Give the coordinates of each transformation of (2, –3). 4. reflection across the y-axis (–2, –3) 5. f(x) = 3(x + 5) – 1 6. f(x) = x 2 + 4x Evaluate.

Holt McDougal Algebra 2 Radical Functions Graph radical functions and inequalities. Transform radical functions by changing parameters. Objectives.

Section 9.3 Day 1 Transformations of Quadratic Functions

Algebra 2 1-8a Exploring Transformations Translations.

Ch. 1 – Functions and Their Graphs 1.4 – Shifting, Reflecting, and Sketching Graphs.

For each function, evaluate f(0), f(1/2), and f(-2)

Radical Functions and Equations ( 무리함수 ) Radical sign index The term is called a radical. The symbol is called a radical sign(sometimes just called radical.

Precalc – 1.5 Shifting, reflecting, and stretching graphs.

Lesson 27 Connecting the parabola with the quadratic function.

Quadratic Functions Unit Objectives: Solve a quadratic equation.

Lesson 13.3 graphing square root functions

Find the x and y intercepts.

13 Algebra 1 NOTES Unit 13.

PIECEWISE FUNCTIONS.

1.6 Transformations of Parent Functions Part 2

Jeopardy Final Jeopardy Domain and Range End Behavior Transforms

I can Shift, Reflect, and Stretch Graphs

Graphing Square Root Functions

Chapter 15 Review Quadratic Functions.

Rev Graph Review Parent Functions that we Graph Linear:

Parent Functions.

Chapter 15 Review Quadratic Functions.

2.7 Graphing Absolute Value Functions

Parent Functions.

SQUARE ROOT Functions 4/6/2019 4:09 PM 8-7: Square Root Graphs.

2.7 Graphing Absolute Value Functions

Functions and Transformations

Horizontal shift right 2 units Vertical shift up 1 unit

Horizontal Shift left 4 units Vertical Shift down 2 units

Predicting Changes in Graphs

1-10 Matching *definitions (4) and the different types of basic graphs (6) *make sure you know the difference between a relation and a function* *make.

15 – Transformations of Functions Calculator Required

The graph below is a transformation of which parent function?

Solving systems of equations by graphing

What is the domain and range for the function f(x) =

Presentation transcript:

Lesson 4.5

The graph of the square root function,, is another parent function that you can use to illustrate transformations. From the graphs below, what are the domain and range of ? Graph on your calculator. You can see that at x=3, f(x)≈

The graph of the square root function,, is another parent function that you can use to illustrate transformations. From the graphs below, what are the domain and range of ? What is the approximate value of at x = 8? How would you use the graph to find ? What happens when you try to find f (x) for values of x < 0?

 In this investigation you first will work with linear functions to discover how to create a new transformation—a reflection. Then you will apply reflections to quadratic functions and square root functions.

Graph on your calculator. a.Predict what the graph of -f 1 (x) will look like. Then check your prediction by graphing f 2 (x)= -f 1 (x). b. Change f 1 to f 1 (x)=-2x-4, and repeat the instructions in part a. c. Change f 1 to f 1 (x)=x 2 +1 and repeat. d. In general, how are the graphs of y=f(x) and y=-f (x) related?

Graph on your calculator. a.Predict what the graph of f 1 (-x) will look like. Then check your prediction by graphing f 2 (x)= f 1 (-x). b. Change f 1 to f 1 (x)=-2x-4, and repeat the instructions in part a. c. Change f 1 to f 1 (x)=x 2 +1 and repeat. d.Change f1 to f1(x)=(x-3) 2 +2 and repeat. Explain what happens. e.In general, how are the graphs of y=f(x) and y=f (-x) related?

a)Predict what the graphs of f 2 =- f 1 (x) and f 3 = f 1 (-x) will look like. Use your calculator to verify your predictions. Write equations for both of these functions in terms of x. b)Predict what the graph of f 4 =-f 1 (-x) will look like. Use your calculator to verify your prediction. c)Notice that the graph of the square root function looks like half of a parabola. Why isn’t it an entire parabola? What function would you graph to complete the bottom half of the parabola? Graph on your calculator.

Reflection of a Function A reflection is a transformation that flips a graph across a line, creating a mirror image. Given the graph of y=f(x), the graph of y=f(-x) is a horizontal reflection across the y-axis, and the graph of -y= f(x), or y=-f(x), is a vertical reflection across the x-axis.

A piecewise function is a function that consists of two or more ordinary functions defined on different domains. Graph

 Enter the equation in your graphing calculator.

Find an equation for the piecewise function pictured at right. For -4≤x≤0, the function appears to be equal to a reflection of the square root function about the y- axis and then shifted one unit up. This would be the function For 0<x≤3, the function appears to be equal to a reflection of the square curve reflected over the x- axis and then shifted one unit to the right and 2 units up.

Find an equation for the piecewise function pictured at right.