Topicmc638239bba3ef95b_1528449000663_0Topic

The symmetry of function plots with respect to the axis X

Levelmc638239bba3ef95b_1528449084556_0Level

Third

Core curriculummc638239bba3ef95b_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).

Timingmc638239bba3ef95b_1528449068082_0Timing

45 minutes

General objectivemc638239bba3ef95b_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesmc638239bba3ef95b_1528449552113_0Specific objectives

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

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 X.

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

Learning outcomesmc638239bba3ef95b_1528450430307_0Learning outcomes

The student:

- transforms the plot of the function in axial symmetry about the axis X.

- 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 X.

Methodsmc638239bba3ef95b_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workmc638239bba3ef95b_1528449514617_0Forms of work

1. Inividual work.

2. Group work.

Lesson stages

Introductionmc638239bba3ef95b_1528450127855_0Introduction

The teacher introduces the subject of the lesson - transforming the plot of the function in axial symmetry about the axis X 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 X.

Proceduremc638239bba3ef95b_1528446435040_0Procedure

Task
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 X 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 X, we need to find images of the greatest amount of points belonging to this plot.mc638239bba3ef95b_1527752263647_0Conclusion:
- In order to find the image of the plot of the given function in the axial symmetry with respect to the axis X, 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 $f\left(x\right)=x^2-4$ for x ∈ {-3, -1, 0, 1, 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 X.

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 X. In groups, they consider the problem on specific examples. They start by analysing the plots from the previous exercise.

Using information they obtained before, they notice that by transforming the point A (x, y) in the axial symmetry about the axis X, they obtain the point A' (x, -y).

Therefore, first coordinates of the points are equal, and the second are opposite. The plot of the obtained function can be written down as y = - f(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:

Students use obtained information in the exercises.

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

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

b) $f\left(x\right)=x^2+1$

c) $f\left(x\right)=\frac{5}{x-3}$

Task
Match in pairs functions whose plots are symmetric with respect to the X axis $f\left(x\right)=3x^2-1,g\left(x\right)=3x^2+1,h\left(x\right)=-3x^2+1,i\left(x\right)=-3x^2-1.$

Task
In the picture there is the plot of the function y = f(x).mc638239bba3ef95b_1527752256679_0In 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 X axis.mc638239bba3ef95b_1527712094602_0Draw the image of the f function in the axial symmetry about the X axis.

Task
Draw the plot of the function $f\left(x\right)=2x+4$ for such arguments x that $-6\le x\le 5$. Identify the domain, the range and the root of the function $g\left(x\right)=-f\left(x\right)$. Check your assumptions by drawing the plot of the function $g$.

An extra task:
The plot of the function $f\left(x\right)=0$ is transformed in axial symmetry about the X axis. Identify the formula of the function whose plot we will obtain.

Lesson summarymc638239bba3ef95b_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:

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 axis of the coordinate systessymmetry about the axis of the coordinate systessymmetry about the axis of the coordinate systes

symmetry of the function plot f(x) about the X axissymmetry of the function plot f(x) about the X axissymmetry of the function plot f(x) about the X axis

symmetry of the point about the X axissymmetry of the point about the X axissymmetry of the point about the X axis

transforming pointstransforming pointstransforming points

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