What’s the Use of It?
Interpretation of Graphs
of Functions
Table of Contents
1.
2.
3.
4.
5.
6.
7.
Objectives
Competences
Finding the values of a function from a graph
Intervals on which a function increases and dicreases
Real life applications
Check your understanding
Bibliography/Sources
Objectives
1- Students will be able to interpret the graphs of
functions.
2- Students will be able to find the values of a
function from a graph.
3- Students will be able to understand the
problems involving the modelling of real life
situations.
Competences
1- The functions whose graphs are given are interpretated.
2- The rules of the functions whose graphs are given are found out.
Finding the values of a function from a graph
Intervals on Which a Function Increases and Decreases
Real Life Applications
Real Life Applications
Real Life Applications
Real Life Applications
• It is a graph showing the profit and
loss condition.
• This graph is not continuously
increasing or decreasing one.
• It shows a decrease between the first
and the fourth years.
• This graph is in increasing situation
between the fourth and fifth years.
• It has reached its minimum value in the
fourth year.
Real Life Applications
• This graph shows the comparison
between fahrenheit and celcius
temparature.
• It is a linear function.
• A regular increase can be observed.
Real Life Applications
• It is a distance-time graph.
• The graph is an increasing function.
• The exchange rate has increased
steadily.
• This graph has reached its maxımum
value in the fifth minute.
• This vehicle has followed an
accelerating movement.
Real Life Applications
• It is a graph showing a ball thrown
up in the air.
• It shows an increase until the
second minute.
• It has reached its maximum value
in the second minute.
• It shows a decrease between the
second and the fourth minute.
Real Life Applications
• This graph shows a change of the
amount of a bill in time.
• It shows 20 £ increase in a minute.
• It has a regular increase.
Check Your Understanding
1-4 The graph of a function f is given. Use the graph to estimate the following.(a) All the
local maximum and minimum values of the function and the value of x at which each occurs.
(b) The intervals on which the function is increasing and on which the function is decreasing.
• A) Minimum and maximum values:
• (-2,-1) minimum value for graph 1
• (-2,2) maximum value for graph 2
• (3,1) maximum value for graph 3
• (-2,3) maximum value for graph 4
• B) The intervals on which the function is increasing and on which the
function is decreasing:
• In the first graph between (-∞ ,-2) and (2,+∞ ) is increasing.
• In the second graph between (-∞ ,-3) is decreasing ; (3,+∞ ) is
increasing.
• In the third graph between (-∞,-2) is decreasing ; (3,+∞) is increasing.
• In the fourth graph between (-∞,-2) is decreasing ; (3,+∞) is
increasing.
Check Your Understanding
• The graph shows the depth of water W in a reservoir over a one-year period as
a function of the number of days x since the beginning of the year.
(a)Determine the intervals on which the function W is increasing and on which it
is decreasing.
(b) At what value of x does W achieve a local maximum? A local minimum?
(c) Find the net change in the depth W from 100 days to300 days.
• a) First 150 days the function is increasing , between 150. and 300.
days the function is decreasing , after the 300. day the function is
increasing.
• b) 150. day W achieves a local maximum and 300. day W achieves a
local minimum.
• c) 75 - 25 = 50
Check Your Understanding
• In order of the piecewise functions :
• Equation of the the first function is y=5
• Equation of the the second function is x-2y-4=0
• Equation of the the third function is x+2y-8=0
Check Your Understanding
• a) f(0)
• b) g(-3)
• c) -2 and 2
Check Your Understanding
• a) g(-2)=4 and g(7)=4
• c) g(-2), g(2), g(7)
• d) x= -1,0,1 and x>7
Check Your Understanding
• a) 80-20=60
• b) 60-35=25
• c) + for digital cameras
- for film cameras
Check Your Understanding
For exercises 1-3, use the graph
1. 94-95
1.2-1.0=0.2 0.2 /1 = 1
2. There is a decrease in this part of the graph.
1.2-1.1=0.1 0.1/1= 0.1
3. The graph is staying constant between 1997-1998.
There is no slope in this period.
Check Your Understanding
• The answer is “c”
Check Your Understanding
Population Growth and Decline The graph shows the population P in a small industrial
city from 1950 to 2000. The variable x represents the number of years since 1950.(a)
Determine the intervals on which the function P is in-creasing and on which it is
decreasing.
What was the maximum population, and in what year was it attained?
a)During the first 25 years the
function is increasing. Between
25. and 50. years the function is
decreasing.
Maximum population is 50
thousands.
Check Your Understanding
The graph gives a sales representative’s distance from his home as a function of time on a
certain day.
(a) Determine the time intervals on which his distance from home was increasing and those
on which it was decreasing.
(b) Describe in words what the graph indicates about his travels on this day.
(a) from 8 a.m. to 9 a.m. the
function is increasing but from 1
to 3 o’clock the function is
decreasing.
(b)The graph gives a sales
representative’s distance from his
home as a function of time on a
certain day.
Bibliography
https://www.boundless.com/biology/textbooks/boundless-biology-textbook/populationand-community-ecology-45/human-population-growth-253/human-population-growth933-12190/
http://www.bbc.co.uk/schools/gcsebitesize/science/aqa_pre_2011/rocks/fuelsrev6.shtml
http://www.cliffsnotes.com/math/basic-math/basic-math-and-pre-algebra/graphs/linegraphs
http://www.rpsoft2000.com/consulting/US-Statistics/recent-charts.htm
http://mathematicsi.com/distance-time-graphs/
http://www.skwirk.com/p-c_s-12_u-213_t-610_c-2270/TAS/7/Sector/conversion/dividedbar/line-and-step/Types-of-graphs/Statistics/Maths/
Applications and Concepts Course 2 - Glencoe Mathematics
Algebra and Trigonometry 3rd edition - James Stewart, Lothar Redlin, Saleem Watson