Worked examples and Exam practice

Slides:

Advertisements

Similar presentations

Functions: Transformations of Graphs Vertical Translation: The graph of f(x) + k appears as the graph of f(x) shifted up k units (k > 0) or down k units.

Advertisements

Lesson 5-8 Graphing Absolute Value Functions

Table of Contents Functions: Transformations of Graphs Vertical Translation: The graph of f(x) + k appears.

3.6 Warm Up Find the initial point, state the domain & range, and compare to the parent function f(x) = √x. y = 3√x – 1 y = -1/2√x y = - √(x-1) + 2.

REFLECTING GRAPHS AND SYMMETRY

2.4 Use Absolute Value Functions and Transformations

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

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

4.3 Reflecting Graphs; Symmetry

Jeopardy Final Jeopardy Parent Functions Equations Stats Other $100

3-2 Families of Graphs Pre Calc A. Parent Graphs.

WHICH TRANSFORMATIONS DO YOU KNOW? ROTATION WHICH TRANSFORMATIONS DO YOU KNOW? ROTATION.

Polynomials and End Behavior

Vertical and Horizontal Shifts of Graphs.  Identify the basic function with a graph as below:

4.1 – 4.3 Review. Sketch a graph of the quadratic. y = -(x + 3) Find: Vertex (-3, 5) Axis of symmetry x = -3 y - intercept (0, -4) x - intercepts.

1.3 Graphs of Functions Equations are mathematical ___________________________. ______________________ are what make the sentences true. A ________________.

Unit 9 Review Find the equation of the axis of symmetry, along with the coordinates of the vertex of the graph and the y-intercept, for the following equation.

2.7 – Use of Absolute Value Functions and Transformations.

f(x) + a x y = f(x) Graphs of Related Functions (1) f(x) = x 2 f(x) +2= x f(x) - 5 = x Vertical Translations.

1 PRECALCULUS Section 1.6 Graphical Transformations.

Mathsercise-C Pie Charts and Scatter Graphs Ready? Here we go!

Translations and reflections of a function

Where am I now? Review for quiz 4.1.

Do-Now What is the general form of an absolute value function?

2.6 Families of Functions Learning goals

Warmup 3-7(1) For 1-4 below, describe the end behavior of the function. -12x4 + 9x2 - 17x3 + 20x x4 + 38x5 + 29x2 - 12x3 Left: as x -,

Transformations of Graphs

ALGEBRA II ALGEBRA II HONORS/GIFTED - SECTIONS 2-6 and 2-7 (Families of Functions and Absolute Value Functions) ALGEBRA II HONORS/GIFTED.

functions graphically

Absolute Value Functions

Reflections of graphs along various lines.

2.6 Translations and Families of Functions

Jeopardy Final Jeopardy Domain and Range End Behavior Transforms

Plenary: rules of indices

Transforming functions

Section 2.5 Transformations.

Transformations of graphs

Lesson 5-1 Graphing Absolute Value Functions

Who Wants to Be a Transformation Millionaire?

Transformations of curves

Warm-up: Sketch the graph of f(x) = x5 – 4x4 + 4x3. Be sure to include all critical values. HW: Quiz Review 2.1/2.2.

-20 is an absolute minimum 6 is an absolute minimum

Day 97 – Exponential Functions: Domain & Range

3.1 EXPONENTIAL & LOG FUNCTIONS

Graph of the derived function

2.7 Graphing Absolute Value Functions

Quadratics graphs.

Topic Past Papers –Functions

F(x) = a b (x – h) + k.

1.5b Combining Transformations

Lesson 9-3: Transformations of Quadratic Functions

Parent Function Transformations

2.7 Graphing Absolute Value Functions

6.4a Transformations of Exponential Functions

Section 5.3: Finding the Total Area

4.1 Notes – Graph Quadratic Functions in Standard Form

Determining the Function Obtained from a Series of Transformations.

Jigsaw Review: 4.1 to 4.3 Friday, Nov. 20, 2009

1.5b Combining Transformations

Unit 3 Functions.

Review 6.1, 6.2, 6.4.

Unit 3 Functions.

Exponential Functions and Their Graphs

6.4c Transformations of Logarithmic functions

15 – Transformations of Functions Calculator Required

The graph below is a transformation of which parent function?

Replacing with and (2.6.2) October 27th, 2016.

Presentation transcript:

Worked examples and Exam practice Transforming graphs Worked examples and Exam practice The animated gifs create immediate interest and can increase a pupil’s attention span worked example 1 worked example 2 worked example 3 worked example 4 worked example 5 Practice question 1 Practice question 2 Practice question 3 Practice question 4

worked example 1 Sketch f(x) - 3 f(x) A (-3, 4) A B (0, 0) f(x) - 3 hit return to see the next step Sketch f(x) - 3 Show where points A, B and C will be on the new graph f(x) A (-3, 4) A B (0, 0) f(x) - 3 C (1, -1) B A (-3, 1) C (1, -4) B (0, -3) C worked example 1

worked example 2 Sketch f(x+4) f(x+4) f(x) A (-1, 0) B (1, -3) hit return to see the next step Sketch f(x+4) Show where points A, B and C will be on the new graph f(x+4) f(x) A (-1, 0) B (1, -3) C (3½, 0) A C A’ (-5, 0) B’ (-3, -3) C’ (-½, 0) B

worked example 3 Sketch -f(x+4) f(x+4) f(x) A (-1, 0) B (1, -3) hit return to see the next step worked example 3 Sketch -f(x+4) Show where points A, B and C will be on the new graph f(x+4) f(x) A (-1, 0) B (1, -3) C (3½, 0) First move 4 along A (-5, 0) B (-3, -3) C (-½, 0) A C Now reflect across x axis A’(-5, 0) B’(-3, 3) C’(-½, 0) B -f(x+4)

worked example 4 2f(x) Sketch 2f(x) f(x) A (-3, 4) A B (0, 0) hit return to see the next step worked example 4 2f(x) Sketch 2f(x) Show where points A, B and C will be on the new graph f(x) A (-3, 4) A B (0, 0) C (1, -1) B A’(-3, 8) C’(1, -2) B’(0, 0) C

worked example 5 Sketch f(4x) A (0, 4) B (8, 0) A B A’ (0, 4) hit return to see the next step Sketch f(4x) Show where points A, B and C will be on the new graph A (0, 4) B (8, 0) A B A’ (0, 4) B’ (2, 0) f(x) f(4x)

Sketch the graph of f(x) + 4 The graph of f(x) = x2+2x - 4 Sketch the graph of f(x) + 4 b) What is the new minimum point of the graph Practice example 1 f(x) Answer (-1,-5)

The graph of f(x) is shown below Practice example 2 The graph of f(x) is shown below Sketch the graph of f(x - 3), mark any relevant points A B C -3 5 f(x) Answer

The graph of f(x) is shown below Practice example 3 The graph of f(x) is shown below Sketch the graph of 2f(x) - 3, note the max point (0,5) Answer f(x)

The graph of f(x) is shown below Practice example 4 The graph of f(x) is shown below Sketch the graph of f(2x), mark any relevant points f(x) -6 3 Answer -6

Practice example 1 Answer The graph of f(x) = x2+2x - 4 Sketch the graph of f(x) + 4 b) What is the new minimum point of the graph f(x) + 4 f(x) b) the new minimum point is (-1,-1) (-1,-5)

Practice example 2 Answer The graph of f(x) is shown below Sketch the graph of f(x - 3), mark any relevant points -3 3 5 8 f(x) f(x-3)

Practice example 3 Answer The graph of f(x) is shown below Sketch the graph of 2f(x) - 3, mark the new max point (0,7) (0,5) f(x) 2f(x)-3

Practice example 4 Answer The graph of f(x) is shown below Sketch the graph of f(2x), mark any relevant points f(2x) f(x) 1.5 -3 -6 3 -6