Topicm8d4348d8de409eb9_1528449000663_0Topic

The symmetry of function plots with respect to the axis Y

Levelm8d4348d8de409eb9_1528449084556_0Level

Third

Core curriculumm8d4348d8de409eb9_1528449076687_0Core curriculum

V. Functions. The student:

12) based on the plot of the function y = f(x) draws plots of functions y = f(x - a), 
y = f(x) + b, y = -f(x), y = f(-x).

Timingm8d4348d8de409eb9_1528449068082_0Timing

45 minutes

General objectivem8d4348d8de409eb9_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm8d4348d8de409eb9_1528449552113_0Specific objectives

1. Transforming the plot of the function in axial symmetry about the axis Y.

2. Identifying the formula of the function whose plot was obtained as a result of transforming the plot of the function in axial symmetry about the axis Y.

3. Communicating in English, developing basic mathematical, computer and scientific competences, developing learning skills.

Learning outcomesm8d4348d8de409eb9_1528450430307_0Learning outcomes

The student:

- transforms the plot of the function in axial symmetry about the axis Y,

- identifies the formula of the function whose plot was obtained as a result of transforming the plot of the function in axial symmetry about the axis Y.

Methodsm8d4348d8de409eb9_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workm8d4348d8de409eb9_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm8d4348d8de409eb9_1528450127855_0Introduction

The teacher introduces the subject of the lesson - transforming the plot of the function in axial symmetry about the axis Y and identifying the formula of the function whose plot was obtained as a result of transforming the plot of the function in axial symmetry about the axis Y.

Students revise the formula for the function whose plot is obtained as a result of transforming the function plot f in axial symmetry about the axis X.

Transforming the plot of the function with respect to the X axis.

- By transforming the plot of the function f in the axial symmetry with respect to the X axis, we obtain the plot of the function g defined by the formula:

Procedurem8d4348d8de409eb9_1528446435040_0Procedure

Students work individually, using computers. Their task is to analyse the way of transforming the plot of the given function in the axial symmetry about the Y axissymmetry about the Y axissymmetry about the Y axis and to draw a conclusion.

[Slideshow]

Conclusion:
- In order to find the image of the plot of the given function in the axial symmetry with respect to the axis Y, we need to find images of the greatest amount of points belonging to this plot.m8d4348d8de409eb9_1527752263647_0Conclusion:
- In order to find the image of the plot of the given function in the axial symmetry with respect to the axis Y, we need to find images of the greatest amount of points belonging to this plot.

Task
Draw the plot of the function f defined by the formula $f\left(x\right)={(x-2)}^2$ for x ∈ {-1, 0, 1, 2, 3}. Then draw a plot of the function g that is created as a result of the transformation of the plot of the function f in the axial symmetry about the axis Y.

Students together think about the formula of the plot created as a result of the transformation of the plot of the function y = f(x) in the axial symmetry about the axis Y. In groups, they consider the problem on specific examples. They answer questions and draw conclusions.

Transforming the plot of the function with respect to the X axis.
- By transforming the plot of the function f in the axial symmetry with respect to the Y axis, we obtain the plot of the function g defined by the formula:m8d4348d8de409eb9_1527752256679_0Transforming the plot of the function with respect to the X axis.
- By transforming the plot of the function f in the axial symmetry with respect to the Y axis, we obtain the plot of the function g defined by the formula:

Students use obtained information in the exercises.

Task
Give the formula of the function g, function whose plot will be obtained by transforming the plot of the function f in axial symmetry with respect to the Y axis.

a) $f\left(x\right)=-3x+2$

b) $f\left(x\right)=-x^2-9$

c) $f\left(x\right)=\frac{2}{x+1}$

Task
In the picture there is the plot of the function y = f(x).

[Illustration 1]

Draw the image of the f function in the axial symmetry about the Y axissymmetry about the Y axissymmetry about the Y axis.

Task
Draw the plot of the function f(x) = -x + 3 for such arguments x that -4 ≤ x ≤ 6. Identify the domain, the range and the root of the function g(x) = f(-x). Check your assumptions by drawing the plot of the function g.

Task
Roots of the function f are numbers -3 and 4. What are roots of the function g whose plot is symmetric with respect to:
a) axis X,
b) axis Y.

An extra task: Choose those functions whose plots are symmetric about the Y axis $f\left(x\right)=x^2+3,h\left(x\right)={(x-4)}^2,z\left(x\right)=x^3,t\left(x\right)=\frac{2}{x^2+3},v\left(x\right)=x+1.$

Lesson summarym8d4348d8de409eb9_1528450119332_0Lesson summary

Students do the revision exercises.

Then together they sum‑up the classes, by formulating the conclusions to memorise.

- By transforming the plot of the function f in the axial symmetry with respect to the X axis, we obtain the plot of the function g defined by the formula:

- By transforming the plot of the function f in the axial symmetry with respect to the Y axis, we obtain the plot of the function g defined by the formula:

Selected words and expressions used in the lesson plan

coordinates of the pointcoordinates of the pointcoordinates of the point

points symmetric about a linepoints symmetric about a linepoints symmetric about a line

symmetry about a linesymmetry about a linesymmetry about a line

symmetry about the X axissymmetry about the X axissymmetry about the X axis

symmetry about the Y axissymmetry about the Y axissymmetry about the Y axis

transforming pointstransforming pointstransforming points

transforming the function plot in the axial symmetry about the Y axistransforming the function plot in the axial symmetry about the Y axistransforming the function plot in the axial symmetry about the Y axis