In this lesson we revise exponential functions from grade 11. Pdf on the zagreb indices of the line graphs of the. Functions and their graphs flashcards from jorge v. Afunctionisincreasing onan interval if for each a,b in the interval, a function is decreasing on an interval if for each a,b in the interval, a value m is the maximum. Apply translations and stretches to the graphs and equations of functions. Question is more of an extension and those ideas will also be established later in this unit if students run out of time today. National 5 n5 mathematics sketching trigonometric graphs. Most applications of mathematics in the sciences and economics involve exponential functions. A graph g consists of a nonempty vertex set v, and an edge set e of unordered 2element sets from v. The constant m is the slope of the linear function and the larger m is in magnitude, the steeper is the graph of f. Relationships between variables using words, tables, graphs, and formulae. The distance between and is b 102 32 109 109 2 9 1 4 1 2. Notes contain examples for teachers to go over on the board and some tasks for pupils to do.
There are past exam questions at the end of the booklet. Ue tshe distance formula to find the distance between two points. Identify the domain, range, and intercepts of a function presented algebraically or graphically. We will start off the chapter with a brief discussion of graphing. Pdf versions of the same file for printing as booklets and issuing to pupils. In the mid 1800s, however, people began to realize that graphs could be used to model many things that were of interest in society. Functions and their graphs mathematics 110 with orock at hudson county community college.
Siyavulas open mathematics grade 10 textbook, chapter 6 on functions covering interpretation of graphs. Apply the function to be graphed elementwise to the input array. Students should work through the graphing basic exponential functions handout. For example, fx 2x is an exponential function with base 2. Identify the equation of a graph from two pairs of coordinates. To solve 53 x 57 2, we note that the bases are the same and so since fx 5x is a onetoone function then we must have 3x 7x 2. Years 810 age 1215 identify the equation of a graph from the gradient and where the line cuts the yaxis. The reflection of a graph in the line y x will be the graph of its inverse. The strands in each course are listed in the graphic. In this chapter well look at two very important topics in an algebra class. The courses in the grade 1112 mathematics curriculum are briefly described below, by course type. An exponential function is a function of the form fx bx where bis a xed positive number.
Step functions are functions that are not continuous. Assume that the outward field has positive sign, and the inward field has negative sign. In this chapter we will be introducing two topics that are very important in an algebra class. Flexible learning approach to physics eee module m1. Functions and graphs you should know the meaning of the terms domain and range of a function. Draw the graph of for using a scale of 2cm to 1 unit on the xaxis and 1 cm to 1 unit on the yaxis. Smartboard files for use on an interactive whiteboard. Grades 1012 program of studies, which can be found on the. The table below shows the average score, m, on the mathematics section of the terra nova.
F ollow in g th e h int, w e start by takin g th e closed p ath 1,2,3,4,5,6 in th e. In sp ection sh ow s th at all vertices h ave d egree 3. Domain and range of inverse functions using graphs grade. Years 810 age 12 15 identify the equation of a graph from the gradient and where the line cuts the yaxis. Use the slopeintercept form to find the slope and yintercept. Algebras bank account 5000 month 2 4 6 8 10 12 14 explain what the xintercept and the yintercept represent. Afunctionisincreasing onan interval if for each a,b in the interval, a function is decreasing on an interval if for each a,b in the interval, a value m is the maximum provided that for every x in the domain, a value m is the minimum provided that for every x in the domain, y x a b c. The far we have considered functions whose graphs are continuous, that is, the graphs have no holes or jumps. Clearly by looking at the graph of the given function fx we could observe that the function fx is increasing in the interval. Oct 01, 2014 domain and range of inverse functions using graphs grade 11 university lesson 1 5 10 1 14. This activity could be completed individually by students or in teams. Formally, a graph g is a nonempty set v together with an irre.
It is essential that all students work through question 12 to master the learning targets for today. Domain and range grade 11 university lesson 1 4 03. Domain and range of inverse functions using graphs grade 11. The table below shows the average score, m, on the mathematics section of the terra nova for brk baumholder, ramstein, kaiserslautern from 2006. Functions and graphs higher maths revision notes goodbye. Ue tshe mdpoii nt formula to find the midpoint of a line segment. Twelfth grade lesson graphing exponential functions. Another example is the function of the floor of x, fxfloorx. This is not really the main topic of this chapter, but we need the basics down before moving into the second topic of this chapter. Formally, a graph g is a nonempty set v together with. First, we will start discussing graphing equations by introducing the cartesian or rectangular coordinates system.
The verticalline test is used to determine whether or not a given graph is a function. Nov 17, 2017 smartboard files for use on an interactive whiteboard. Ue as cnaodoir te plane and geometric formulas to model and solve reallife problems. Create an array of values to serve as function inputs and assign the array into a variable. Notes contain examples for teachers to go over on the. However, the response matrix only provides information about the total conductivity. In this paper, we investigate topological indices of the line graphs of the tadpole graphs, wheel graphs and ladder graphs using the subdivision concept, which generalize the results of ranjini et.
1209 219 1385 562 291 139 454 1584 1555 833 1243 417 1008 786 487 114 888 818 1283 1252 1352 923 1366 108 1065 692 996 263 136 641 402