Topicm4299c733058dc6e7_1528449000663_0Topic

Translating plots of functions along the X axis or the Y axis

Levelm4299c733058dc6e7_1528449084556_0Level

Third

Core curriculumm4299c733058dc6e7_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).

Timingm4299c733058dc6e7_1528449068082_0Timing

45 minutes

General objectivem4299c733058dc6e7_1528449523725_0General objective

Using mathematical objects, interpreting mathematical concepts.

Specific objectivesm4299c733058dc6e7_1528449552113_0Specific objectives

1. Translating the plot of the function along axes of the coordinate system.

2. Finding formulas of functions whose plots are obtained as a result of translating the plot of the function along axes of the coordinate system.

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

Learning outcomesm4299c733058dc6e7_1528450430307_0Learning outcomes

The student:

- translates the plot of the function along axes of the coordinate system,

- finds formulas of functions whose plots are obtained as a result of translating the plot of the function along axes of the coordinate system.

Methodsm4299c733058dc6e7_1528449534267_0Methods

1. Discussion.

2. Chain of associations.

Forms of workm4299c733058dc6e7_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionm4299c733058dc6e7_1528450127855_0Introduction

The teacher introduces the subject of the lesson – translating the plot of the function along the X axis or the Y axis and identifying formulas of functions whose plots we obtain in such way.

Procedurem4299c733058dc6e7_1528446435040_0Procedure

Task
Students work individually, using computers. Their task is to find the image of the plot of the function in translation along the X axis or the Y axis.

[Geogebra applet]

Students work with the method of the chain of associations. They obtain a chain drawn on a big cardboard, that consists of empty links. They fill the links with terms, formulas and associations connected with translating plots of functions along axes of the coordinate system.

Students present their chains and discuss the most important links.

The conclusion students should make:

- By translating the plot of the function f by p units to the right along the X axis, we obtain the plot of the function g described with the formula g(x) = f(x − p).

- By translating the plot of the function f by q units up along the Y axis, we obtain the plot of the function h described with the formula h(x) = f(x) + q.

Students work in groups. They take part in the thematical contest. The group that solves obligatory tasks correctly obtains two pluses. If the group solves the extra task as well, they obtain two more pluses.

Contest task
The drawing shows the plot of the function f.

[Illustration 1]

Draw plots of functions:

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

b) $h\left(x\right)=f(x+3)$,

c) $s\left(x\right)=f\left(x\right)+1$,

d) $z\left(x\right)=f\left(x\right)-4$.

Contest task
Give the formula of the function whose plot is obtained as a result of translating the plot of the function:
a) f(x) = 2x by 2 units to the right along the X axis,
b) f(x) = x + 1 by 4 units to the left along the X axis,
c) f(x) = 5x by 3 units down along the Y axis.m4299c733058dc6e7_1527752263647_0Give the formula of the function whose plot is obtained as a result of translating the plot of the function:
a) f(x) = 2x by 2 units to the right along the X axis,
b) f(x) = x + 1 by 4 units to the left along the X axis,
c) f(x) = 5x by 3 units down along the Y axis.

Contest task
There is the formula of the functionformula of the functionformula of the function f(x) = 2x - 4. Give formulas of functions:

a) f(x + 1),

b) f(x - 3),

c) f(x) - 5,

d) f(x) + 4.

Contest task 
There is the formula of the functionformula of the functionformula of the function f(x) = 2x - 1. Give formulas of functions:

a) f(x - 6),

b) f(x) + 2.

Contest task
[Illustration 2]

There is the function f.
By how many units along the X axis and the Y axis we need to move the plot of the function for it to have:
a) one root,
b) no roots.m4299c733058dc6e7_1527752256679_0There is the function f.
By how many units along the X axis and the Y axis we need to move the plot of the function for it to have:
a) one root,
b) no roots.

An extra contest task:
The plot of the function f defined with the formula $f\left(x\right)=\frac{-2}{x}$ has been moved by p units along the X axis and by q units along the Y axis, as a result we obtained the formula of a function $g\left(x\right)=\frac{-2}{x+4}-3$. Give values of p and q.m4299c733058dc6e7_1527712094602_0An extra contest task:
The plot of the function f defined with the formula $f\left(x\right)=\frac{-2}{x}$ has been moved by p units along the X axis and by q units along the Y axis, as a result we obtained the formula of a function $g\left(x\right)=\frac{-2}{x+4}-3$. Give values of p and q.

Lesson summarym4299c733058dc6e7_1528450119332_0Lesson summary

Students do the revision exercises.

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

- By translating the plot of the function f by p units to the right along the X axis, we obtain the plot of the function g described with the formula g(x) = f(x − p).

- By translating the plot of the function f by q units up along the Y axis, we obtain the plot of the function h described with the formula h(x) = f(x) + q.

Selected words and expressions used in the lesson plan

formula of the functionformula of the functionformula of the function

rootrootroot

the greatest valuethe greatest valuethe greatest value

translation of the plot of the function f by p units along the X axistranslation of the plot of the function f by p units along the X axistranslation of the plot of the function f by p units along the X axis

translation of the plot of the function f by q units along the Y axistranslation of the plot of the function f by q units along the Y axistranslation of the plot of the function f by q units along the Y axis