Functions and Their Graphs REPRESENTING RELATIONS AND FUNCTIONS

2011

2013

The domain of a function is the set of x values (along the x-axis) that gives a valid answer (y value) when the function is evaluated. Also, the set of all x values must be mapped to one and only one y value.

In exercises requiring estimations or approximations, your answers may vary slightly from the answers given here. 1. (a) The point (−1, −2) is on the graph of f , so f (−1) = −2. (b) When x = 2, y is about 2.8, so f (2) ≈ 2.8. (c) f (x) = 2 is equivalent to y = 2. When y = 2, we have x = −3 and x = 1. (d) Reasonable estimates for x when y = 0 are x = −2.5 and x = 0.3. (e) The domain of f consists of all x-values on the graph of f. For this function, the domain is −3 ≤ x ≤ 3, or [−3, 3].

International Journal of Advanced Science and Engineering, 2023

The concept of function is one of the fundamental mathematical concepts, very important within mathematics itself as well as in the application of mathematics. Functions are an essential element of mathematical structuring and modeling of problems (e.g.in algebraic structures), as well as a means of comparing structures thus obtained (eg homomorphisms of structures). A mathematical function is a rule that gives the value of the dependent variable corresponding to certain values of one or more independent variables. A function can be represented in several ways, such as a table, formula, or graph. Apart from isolated points, the mathematical functions found in physical chemistry are single-valued. Apart from isolated points, the mathematical functions that occur in physical chemistry are continuous.

International Journal of Scientific & Engineering Research,, 2017

This study presents investigation of difficulties of grade nine students have on the concept of function using a descriptive survey method. Both quantitative and qualitative research approaches were used to explore the students’ challenges in this study. Data was collected using test, interview and teachers’ questionnaire. The four commonly used ways to represent function is then used to analyse students’ interpretation and manipulation in different contexts. The finding of the study reviled that students have difficulties in basic definition of function, to identify the difference between function and relation, difficulty to identify an equation with two variables x and y as a function or not. The students have also difficulty in verbal and graphical representation of function. Identified students misunderstanding about the function concept are: any functions should contain both x and y variables, any continuous graph are a function and a discontinuous graph is not a function. This could be because of students’ attention to the lesson, their background weakness and students limited English language skills. Based on the findings of the study different recommendations are suggested in order to solve the problems.

1. f (−5) = (−5) 2 − 1 = 25 − 1 = 24 f (− √ 3) = (− √ 3) 2 − 1 = 3 − 1 = 2 f (3) = (3) 2 − 1 = 9 − 1 = 8 f (6) = (6) 2 − 1 = 36 − 1 = 35 2. f (−5) = −2(−5) 2 + (−5) = −2(25) − 5 = −55 f (− 1 2) = −2(− 1 2) 2 + (− 1 2) = −2(1 4) − 1 2 = −1 f (2) = −2(2) 2 + (2) = −2(4) + 2 = −6 f (7) = −2(7) 2 + (7) = −2(49) + 7 = −91 3. f (−1) = √ −1 + 1 = √ 0 = 0 f (0) = √ 0 + 1 = √ 1 = 1 f (3) = √ 3 + 1 = √ 4 = 2 f (5) = √ 5 + 1 = √ 6 4. f (− 1 2) = ï¿¿ 2(− 1 2) + 4 = √ −1 + 4 = √ 3 f (1 2) = ï¿¿ 2(1 2) + 4 = √ 1 + 4 = √ 5 f (5 2) = ï¿¿ 2(5 2) + 4 = √ 5 + 4 = √ 9 = 3 f (4) = ï¿¿ 2(4) + 4 = √ 8 + 4 = √ 12 = 2 √ 3 2

A simple and easily understandble introduction to set, relation and function

Formalized Mathematics, 1990

Summary. The article is a continuation of [1]. We define the following concepts: a function from a set X into a set Y, denoted by “Function of X, Y”, the set of all functions from a set X into a set Y, denoted by Funcs (X, Y), and the permutation of a set (mode Permutation of X, ...

2011

This communication focuses on the activity of two secondary school students in a task involving the concept of function and transformations of functions of the type () p x k  and () p x h  , and analyses the role of the graphic calculator. The results suggest that students are beginning to have an object-oriented view of function. Concerning the transformation () p x k  they have already established the operational invariants, and it seems that the graphic calculator played an important role in that.