FUNCTION CROSSWORD
Complete the cross word.
CLUES
TOWARD THE DESCRIPTION OF A FUNCTION
Match each word of the first column, with the correct definition of the second column. Write your match in
the third column
MATHEMATICAL OBJECT
DEFINITION
A. domain
1. The points where the function intersects an
axis
B. RANGE
2. The point where, as you move across the
graph from left to right, the function goes
down and then goes up
C. SLOPE
3. The set of all outputs or y-values for a
function
D. INTERCEPTS
(WITH THE X OR Y
AXIS)
4. As you move across the graph from left to
right, the graph goes down
E. F(X) IS INCREASING
OVER AN INTERVAL
5. The point where, as you move across the
graph from left to right, the function goes up
and then goes down
F. F(X) IS DECREASING
OVER AN INTERVAL
6. The set of input values of the variable x
G. MINIMUN
7. As you move across the graph from left to
right, the graph goes up.
H. MAXIMUM
8. The steepness of a line or the rate of change
of a linear relationship
Answers:
A6; B3; C8; D1; E7; F4; G2; H5
WORKSHEET 3: The Leaky pool
Group A
The graph shows that the water level , depth d, changes over a 15-hour time period (domain: 0  t  15 ).
https://pixabay.com/it/piscina-costa-rica-hotel-857179/
Number the descriptions according to what is happening first
Time order
What’s happening?
a. At t  12 , the water reaches its highest level at just about 5 meters, so d=5
b. The water level rises for the next 6 hours, during the interval 6  t  12
c. During the first 6-hour interval ( 0  t  6 ), the water level drops. The leak
seems to get worse as time passes
d. When t  5.2 and d  0.8 , it seems that someone starts to refill the pool
e. At the beginning, when no time has passed, t=0, the water in the pool is 2
meter deep, so d  2
f. At the 12-hour mark, the in-flowing water is apparently turned off because,
since the pool still has a leak, the water level starts to drop again
WORKSHEET 3: The Leaky pool
Group B
The graph shows that the water level , depth d, changes over a 15-hour time period (domain: 0  t  15 ).
https://pixabay.com/it/piscina-costa-rica-hotel-857179/
Number the properties of the function according to what you would say first to describe the
graph
Order
Function properties
a. The function has a minimum at 5.2 ; 0.8
b. The function is increasing over the interval 6  t  12
c. The function has a maximum at 12 ; 5
d. The point 2 ; 0 is the intercept of the function with the y-axis.
e. The function is decreasing over the interval 12  t  15
f. The function is decreasing over the interval 0  t  5.2
NATURAL and SCIENTIFIC LANGUAGE
NATURAL LANGUAGE
SCIENTIFIC LANGUAGE
PRECISE
INDEFINITE
UNIVOCAL
AMBIGUOUS
ABSTRACT
CONTEXTUALIZED
SYNTHETIC
ANALITIC
NATURAL and SCIENTIFIC LANGUAGE
SYNTHETIC
PRECISE
CONTEXTUALIZED
ANALITIC
ABSTRACT
INDEFINITE
UNIVOCAL
AMBIGUOUS
Complete the T-chart below, inserting the adjectives that best describe the natural or the scientific language.
NATURAL LANGUAGE
SCIENTIFIC LANGUAGE
TOWARD THE DESCRIPTION OF A FUNCTION
MATHEMATICAL OBJECT
A. DOMAIN
1. The set of input values of the variable x
B. RANGE
2. The set of all outputs or y-values for a
function
C. SLOPE
3. The steepness of a line or the rate of change
of a linear relationship
D. INTERCEPTS
(WITH THE X OR Y
AXIS)
4. The points where the function intersects an
axis
E. F(X) IS INCREASING
OVER AN INTERVAL
5. As you move across the graph from left to
right, the graph goes up.
F. F(X) IS DECREASING
OVER AN INTERVAL
6. As you move across the graph from left to
right, the graph goes down
G. MINIMUN
H. MAXIMUM
Answers:
DEFINITION
A6; B3; C8; D1; E7; F4; G2; H5
7. The point where, as you move across the
graph from left to right, the function goes
down and then goes up
8. The point where, as you move across the
graph from left to right, the function goes up
and then goes down
WORKSHEET: DESCRIBING LINEAR FUNCTION AND PARABOLA
Complete the following test with the missing appropriate mathematical terms.
LINEAR FUNCTION
Its graph is a straight line. It is describe by the expression y  mx  q .
The domain of the function is R (set of real numbers).
q is the intersect with the y-axis. If y  0 then the graph passes through the origin (line a).
m is called the slope of the function.

If m  0 then the function is increasing (lines b, c)

If m  0 then the function is constant (lines d) and the graph is parallel to the x-axis.

If m  0 then the function is decreasing (lines e)
WORKSHEET: DESCRIBING LINEAR FUNCTION AND PARABOLA
Complete the following test with the missing appropriate mathematical terms.
LINEAR FUNCTION
Look at the linear functions in the graph below:
Linear function’s graph is a straight line. It is describe by the expression y  mx  q .
The domain of the function is R (set of real numbers).
q is the intersect with the y-axis. If y  0 then the graph passes through the origin (line a).
m is called the slope of the function.

If m  0 then the function is increasing (lines a, b)

If m  0 then the function is constant (line c) and the graph is parallel to the x-axis.

If m  0 then the function is decreasing (line d)
PARABOLA
Look at the parabolas in the graph below:
Parabolas are described by the function y  ax 2  bx  c with a  0 .
The domain of the function is R and therefore there must be an intersect with y-axis. If y  0 then
the graph passes through the origin (parabola a).
If a  0 then the graph looks like a U (parabolas b,d,e) and the function has a minimum.
If a  0 then the graph looks like a bow (parabola a,c) and the function has a maximum.
If either the minimum is below the x-axis (parabola b) or the maximum is above the x-axis
(parabola a), then the function has two zeros, that represent the intersects with the x-axis: this
occurs when   b 2  4ac is greater than 0.
If  is equal to 0, there is only one intersect with the x-axis (parabola e).
If  is less than 0, there are no intercepts with the x-axis (parabolas c, d).
WORKSHEET: DESCRIBING LINEAR FUNCTION AND PARABOLA
Complete the following test with the missing appropriate mathematical terms.
LINEAR FUNCTION
Look at the linear functions in the graph below:
Linear function’s graph is a straight line. It is describe by the expression y  mx  q .
The domain of the function is _______.
q is the ___________ with the y-axis. If y  0 then the graph passes through the ___________
(line a).
m is called the ___________ of the function.

If m  0 then the function is ___________________ (lines a, b)

If m  0 then the function is ___________________(line c) and the graph is parallel to the xaxis.

If m  0 then the function is ____________________ (line d)
PARABOLA
Look at the parabolas in the graph below:
Parabolas are described by the function y  ax 2  bx  c with a  0 .
The ___________ of the function is R and therefore there must be an ___________ with y-axis. If
y  0 then the graph passes through the ___________ (parabola a).
If a  0 then the graph looks like a U (parabolas b,d,e) and the function has a ___________.
If a  0 then the graph looks like a bow (parabola a,c) and the function has a ___________.
If either the minimum is ___________ the x-axis (parabola b) or the maximum is ___________
the x-axis (parabola a), then the function has two zeros, that represent the _________________
with the x-axis: this occurs when   b 2  4ac is ______________ 0.
If  is _______________ 0, there is only one intersect with the x-axis (parabola e).
If  is _______________ 0, there are no intercepts with the x-axis (parabolas c, d).