PRESENTED BY:STUDENT NAMES

• MUHAMMAD IMRAN• KALEEM ULLAH• DILAWAR GULL• SUFYAN MAQSOOD• ANAS REHMAN

GRAPH OF FUNCTION

PRESENTED TO: SIR WAJID

• What is graph of a function?A good way of presenting a function is by graphical representation.

Graphs give us a visual picture of the function. The most common way to graph a function is to use the rectangular co-ordinate system. This consists of:

• The x-axis;• The y-axis;• The origin (0,0); and• The four quadrants, normally labelled I, II, III, IV.

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GRAPH OF FUNCTION

• Normally, the values of the independent variable (generally the x-values) are placed on the horizontal axis, while the values of the dependent variable (generally the y-values) are placed on the vertical axis.

• The x-value, called the abscissa, is the perpendicular distance of P from the y-axis.

• The y-value, called the ordinate, is the perpendicular distance of P from the x-axis.

• The values of x and y together, written as (x, y) are called the co-ordinates of the point P.

• It's called the "rectangular" coordinate system

• Cartesian Coordinate system

Rene Descartes

The x-y coordinate system is also called the Cartesian Coordinate system, after its developer, Rene Descartes (1596 - 1650). This graphing system was incredibly important for the advancement of science and engineering.

Graph of a function• In the real world, it's very common that one quantity depends on another quantity.

• For example, if you work in a fast food outlet, your pay packet depends on the number of hours you work. Or, the amount of concrete you need to order when constructing a building will depend on the height of the building.

• The graph of a function is really useful if we are trying to model a real-world problem. ("Modeling" is the process of finding the relationships between quantities.)

• Sometimes we may not know an expression for a function but we do

know some values (maybe from an experiment). The graph can give

us a good idea of what function may be applied to the situation to

solve the problem.

• Example where use ?• In everyday life, many quantities depend on one or more changing variables. For example:• (a) Plant growth depends on sunlight and rainfall• (b) Speed depends on distance travelled and time taken• (c) Voltage depends on current and resistance

PROCEDURE OF GRAPH

• The graph of a function is the set of all points whose co-ordinates (x, y) satisfy the function y=f(x). This means that for each x-value there is a corresponding y-value which is obtained when we substitute into the expression for f(x).

• Since there is no limit to the possible number of points for the graph of the function, we will follow this procedure at first:

• Select a few values of x (at least 5)• Obtain the corresponding values of the function and enter them into

a table• Plot these points by joining them with a smooth curve

Continuous and Discontinuous Functions

• Continuous Functions• Consider the graph of f(x) =x^2

• We can see that there are no "gaps" in the curve. Any value of x will give us a corresponding value of y. We could continue the graph in the negative and positive directions, and we would never need to take the pencil off the paper.

• Such functions are called continuous functions

• In simple English: The graph of a continuous function can be

drawn without lifting the pencil from the paper.

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Discontinuities Functions

• Now consider the function f(x)= x^2 x<1 , f(x)=6-x x > 1,

• We note that the curve is not continuous at x=2

• For a function to be continuous at a point, the function must exist at the point and any small change in x produces only a small change in f(x).

LINEAR Function

• These are functions of the form:

• y = m x + b,

• where m and b are constants. A typical use for linear functions is converting from one quantity or set of units to another. Graphs of these functions are straight lines. m is the slope and b is the y intercept. If m is positive then the line rises to the right and if m is negative then the line falls to the right.

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QUADRATIC FUNCTION

• These are functions of the form:

• y = a x ʌ2+ b x + c,

• where a, b and c are constants. Their graphs are called parabolas. This is the next simplest type of function after the linear function. Falling objects move along parabolic paths. If a is a positive number then the parabola opens upward and if a is a negative number then the parabola opens downward.

POLYNOMIAL FUNCTION

• These are functions of the form:

• y = an · x n + an −1 · x n −1 + … + a2 · x 2 + a1 · x + a0,

• where an, an −1, … , a2, a1, a0 are constants. Only whole number powers of x are allowed. The highest power of x that occurs is called the degree of the polynomial

• Polynomials are useful for generating smooth curves in computer graphics application.

• . Example Graph the polynomial function x3 – 2x2 – 3x .

• Table of points

USES OF GRAPH IN DAILY LIFE

• The use of graphs in the household• They can show what meals should be cooked and can help construct a shopping list when certain

meals are entered into a graph.

• Graphs can be used to show which activities will be completed on which day or even how much pocket money will be assigned to each child in the family

• The use of graphs in the media• Graphs are also used on TV shows, particularly informative shows and the news, to reveal facts

and figures to the audience. Graphs can be used to show weather trends or trends in the economy.

• USE IN SPORTS• They can also be used to reveal sports scores and reveal how particular teams are doing in

comparison to other teams.

• Like in a cricket

THANK YOU…