IDENTIFYING FUNCTIONS USING GRAPHS

Identifying functions using graphs :

Graphs can be used to display relationships between two sets of numbers. Each point on a graph represents an ordered pair. The first coordinate in each ordered pair is the input value. The second coordinate is the output value. The graph represents a function if each input value is paired with only one output value.

Identifying functions using graphs - Examples

Example 1 :

The graph given below shows the relationship between the number of hours students spent studying for an exam and the marks scored in the exam. Determine whether the relationship represented by the graph is a function.

Solution :

From the graph, it is clear that if a students spends 2 hours for studying, he will be able to score 70 marks in the exam. And if he spends 9 hours for studying, he will be able to score 90 marks in the exam.

So, we can consider the number of hours of studying as input values and marks scored in the exam as output values.

The points represent the following ordered pairs in the form (input, output) or (x, y) :

(1, 70), (2, 70), (2, 85), (3, 75), (5, 80), (6, 82), (7, 88), aaaa(9, 90), (9, 95) and (12, 98).

In the above order pairs, there is only one output value for each input value. And no input value has more than one output value.

Since, there is only one output value for each input value, the relationship represented by the graph is a function.

Example 2 :

The graph shows the relationship between the heights and weights of the members of a basketball team. Is the relationship represented by the graph a function ? Explain.

Solution :

From the graph, it is clear that if the height of a member is 73 inches, his weight will be 180 lbs.

So, we can consider the height as input value and weight as output value.

The points represent the following ordered pairs in the form (input, output) or (x, y) :

(68, 160), (70, 165), (70, 175), (71, 170), (71, 185), (73, 180) and (74, 190)

Notice that 70 is paired with both 165 and 175, and 71 is paired with both 170 and 185. These input values are paired with more than one output value

Since, there is more than one output value for the input values 70 and 71, the relationship represented by the graph is not a function.

After having gone through the stuff given above, we hope that the students would have understood "Identifying functions from graphs".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6