Topicmf80ecc1e2a641e8f_1528449000663_0Topic

The output of the functionfunctionfunction for the given inputinputinput

Levelmf80ecc1e2a641e8f_1528449084556_0Level

Third

Core curriculummf80ecc1e2a641e8f_1528449076687_0Core curriculum

V. Functions. The student:

4) finds the following information in the graph of the functiongraph of the functiongraph of the function: the domain, the root, the ranges of monotonicity, the ranges, in which the function takes values greater (not smaller) or smaller (not greater) than a given number, the greatest and the smallest outputs of a functionfunctionfunction (if they exist) in a given closed interval and the inputs for which the greatest and the smallest outputs are taken by the function.

Timingmf80ecc1e2a641e8f_1528449068082_0Timing

45 minutes

General objectivemf80ecc1e2a641e8f_1528449523725_0General objective

Interpretation and the use of information presented both in a mathematical and popular science texts also using graphs, diagrams and tables.

Specific objectivesmf80ecc1e2a641e8f_1528449552113_0Specific objectives

1. Communication in English, developing mathematical, IT and basic scientific and technical competence, developing learning skills.

2. Calculating the input of the functionfunctionfunction for a given output.

3. Reading the output for a given input from a graph.

Learning outcomesmf80ecc1e2a641e8f_1528450430307_0Learning outcomes

The student:

- calculates the input of the functionfunctionfunction for a given output,

- reads the output for a given inputinputinput from a graph.

Methodsmf80ecc1e2a641e8f_1528449534267_0Methods

1. Mind map.

2. Task competition.

Forms of workmf80ecc1e2a641e8f_1528449514617_0Forms of work

1. Individual work.

2. Group work.

Lesson stages

Introductionmf80ecc1e2a641e8f_1528450127855_0Introduction

Students work in groups making mind maps with all they know about the functionfunctionfunction and methods of describing the function.

Then, they present their posters.

The teacher verifies the information and explains any doubts.

Proceduremf80ecc1e2a641e8f_1528446435040_0Procedure

The teacher informs the students that the aim of the class is calculating the output of the functionfunctionfunction for a given inputinputinput.

Discussion – how to calculate the output of the function described by a formula?

The students formulate hypotheses, check them and write down the conclusion.

Conclusion:

If a function is described by a formula, calculating the output of the function for a given input can be done by substituting the input into the formula and calculating the value of the arithmetic expression that you get.mf80ecc1e2a641e8f_1527752263647_0If a function is described by a formula, calculating the output of the function for a given input can be done by substituting the input into the formula and calculating the value of the arithmetic expression that you get.

The students solve the tasks individually to consolidate their knowledge.

Task
Calculate the output of the functionfunctionfunction $f\left(x\right)=5x-3$ for inputs from set $\left\{-3;-2,2;0,8;\sqrt{5}\right\}$.
Answer: $f(-3)=-18,f(-2,2)=-14,f(0,8)=1,f\left(\sqrt{5}\right)=5\sqrt{5}-3$.

Task
Working in groups, the students guess how to read the output for a given inputinputinput from the graph. They analyse the material shown in and interactive presentation. They formulate their hypotheses and conclusions.

[Slideshow]

Conclusion:

In order to read the output for a given input from the graph you need to draw a line x = xIndeks dolny k_k, where xIndeks dolny k_k – given input, until the intersection with the graph of the function. The other coordinate of the common point of the line x = xIndeks dolny k_k and the graph of the function is the output of the function for the given input.mf80ecc1e2a641e8f_1527712094602_0In order to read the output for a given input from the graph you need to draw a line x = xIndeks dolny k_k, where xIndeks dolny k_k – given input, until the intersection with the graph of the function. The other coordinate of the common point of the line x = xIndeks dolny k_k and the graph of the function is the output of the function for the given input.

The students use the information to take part in the problem solving competition.

Competition tasks.

Task
Function f is described by formula $f\left(x\right)=\frac{x+2}{3}$. Calculate the output of this functionfunctionfunction for inputs from set $\left\{-3;-\frac{2}{3};0;3,5\right\}$.

Task
Function g is represented by formula $g\left(x\right)=\frac{x^2+2}{4}$. Check which of points $A(-1;\frac{3}{4}),B(0;\frac{4}{3}),C(2;1,5),D(3;3)$ are on the graph of this functionfunctionfunction.

Task
Function f is represented by formula $f\left(x\right)=\frac{x-7}{x^2+1}$, where $x\in \left\{-2,-1,0,1,2\right\}$. Give the set of outputsset of outputsset of outputs of this function.

Task
In functionfunctionfunction h every natural number from set $\left\{1,2,3,4,5,6,7,8\right\}$ is associated to the remainder of the number divided by 3. Give the set of outputsset of outputsset of outputs of this function.

Task
Sketch the graph of function k, which satisfies the following conditions at the same time: .

Finally, the teacher checks if the students’ results were correct and explains any doubts. Three fastest students get marks.

An extra task
Function g is described by formula $g\left(x\right)=-x+3$ for $x\in C$. Which of the given numbers: - 0,5; 4; 5,75; 8 can be the outputs of this functionfunctionfunction? Justify your answer.
Answer: numbers 4 i 8.

Lesson summarymf80ecc1e2a641e8f_1528450119332_0Lesson summary

Students do the consolidation tasks.

Finally, they recapitulate the class and formulate the conclusions to be remembered.

- If a function is described by a formula, calculating the output of the function for a given input can be done by substituting the input into the formula and calculating the value of the arithmetic expression that you get.
- In order to read the output for a given input from the graph you need to draw a line x = xIndeks dolny k_k, where xIndeks dolny k_k – given input, until the intersection with the graph of the function. The other coordinate of the common point of the line x = xIndeks dolny k_k and the graph of the function is the output of the function for the given input.mf80ecc1e2a641e8f_1527752256679_0- If a function is described by a formula, calculating the output of the function for a given input can be done by substituting the input into the formula and calculating the value of the arithmetic expression that you get.
- In order to read the output for a given input from the graph you need to draw a line x = xIndeks dolny k_k, where xIndeks dolny k_k – given input, until the intersection with the graph of the function. The other coordinate of the common point of the line x = xIndeks dolny k_k and the graph of the function is the output of the function for the given input.

Selected words and expressions used in the lesson plan

coordinate systemcoordinate systemcoordinate system

domain of the functiondomain of the functiondomain of the function

functionfunctionfunction

graph of the functiongraph of the functiongraph of the function

inputinputinput

set of outputsset of outputsset of outputs