Jeopardy - functions
Identifying
Function
Functions Characteristics
Linear
Functions
Linear
Equations &
Inequalities
Non-Linear
Functions
Q $100
Q $100
Q $100
Q $100
Q $100
Q $200
Q $200
Q $200
Q $200
Q $200
Q $300
Q $300
Q $300
Q $300
Q $300
Q $400
Q $400
Q $400
Q $400
Q $400
Q $500
Q $500
Q $500
Q $500
Q $500
Final Jeopardy
$100 Question from Identifying
Functions
Which of the following relations is a function?
I. {(0,0), (0,1), (0,2)}
II. {(0,0), (1,1), (2,4)}
III. {(0,0), (1,2), (2,2)}
IV. {(0,0), (1,2), (1,3)}
$100 Answer from Identifying
Functions
II and III
$200 Question from Identifying
Functions
A video club costs $25 to join. Each video that is
rented costs $2.50. Let v represent the number
of videos. Identify the independent and
dependent variables. Then, write an equation, in
function notation, for the situation.
$200 Answer from Identifying
Functions
Independent: videos rented
Dependent: total cost
f(v) = 2.5v + 25
$300 Question from Identifying
Functions
The temperature of air in a room is 55˚F.
The thermostat is adjusted so that the temperature
increases by 8˚F per hour. Write a function that
describes the temperature of the air over time.
Create a table of values to show the temperature
change over the first several hours.
$300 Answer from Identifying
Functions
y = 8x + 55
Time
(Hours)
1
3
5
7
9
11
Temp
(˚F)
63
79
95
111
127
146
$400 Question from Identifying
Functions
The line graph represents the price of a type of
personal computer over a five-year period. Why the
graph is misleading? What might someone believe
because of the graph?
Computer Price
$2000
$1900
$1800
$1600
$800
2002 2003 2004 2005 2006
$400 Answer from Identifying
Functions
The graph is misleading because the intervals on
the vertical axis are not equal.
Someone might believe that the price declined
quickly from 2002 to 2004, then more slowly.
In fact, the price declined $200 each year.
•Graph -2x + 4y = 4 for the domain D: {-8, -4, 0, 4, 8}
$500 Question from Identifying
Functions
Graph -2x + 4y = 4
$500 Answer from Identifying
Functions
y
8
6
4
2
–8
–6
–4
–2
–2
–4
–6
–8
2
4
6
8
x
$100 Question from Function
Characteristics
What is the
domain of the
function
graphed at the
right?
$100 Answer from Function
Characteristics
0<x≤5
$200 - Function Characteristics
The relationship between the weight of an object on the
Moon and on Earth is given by the function y = 6x where x
is the weight of the object on the Moon and y is the weight
of an object on Earth. Determine the domain and range of
this function.
A. D: {x ≥ 0}; R: {y ≥ 6}
B. D: {x ≥ 0}; R: {y ≥ 0}
C. D: {x ≥ 6}; R: {y ≥ 0}
D. D: {x ≤ 0}; R: {y ≤ 6}
$200 - Function Characteristics
B. D: {x ≥ 0}; R: {y ≥ 0}
$300 - Function Characteristics
The scatterplot below shows the relationship between the volume of water sealed
in a boiler and the temperature of the steam generated. Select the statements
that are supported by this data.
I.
As the volume of water is
decreased, the temperature inside
the boiler increases
II. Temperature and volume have a
positive correlation
III. Temperature and volume have a
negative correlation
IV. As the volume of water is
increased, the temperature inside
the boiler decreases
$300 - Function Characteristics
I, III, and IV
$400 - Function Characteristics
What is the value of the function
when the input is 2?
$400 Answer from Function
Characteristics
f(2) = -3/4
$500 -Function Characteristics
The table below shows the value of a term in a given
position in a number sequence. If the sequence follows a
pattern, which expression best represents the value of the nth
term?
Value of
Position
term
1
2
6
3
4
24
5
n
?
$500 - Function Characteristics
C.
$100 - Linear Functions
The line segment on the graph below shows the altitude
of a landing plane from the time its wheels are lowered to
the time its wheels touch the ground. Which of the
following best describes the slope of the line segment?
A. The plane descends 1 foot per 8
seconds
B. The plane descends about 8 feet
per second
C. The plane descends 1 foot per 2
seconds
D. The plane descends about 2 feet per
second.
$100 - Linear Functions
B. The plane descends about
8 feet per second
$200 - Linear Functions
The equation of a line is given by 6x + 3y = 6. What must happen to
the slope and y-intercept if the equation of the line is transformed to
3y – 4x = -6? (Hint! Change to slope-intercept form to compare.)
A. The slope is unchanged and the y-intercept is divided by 3.
B. The slope is multiplied by - 2/3, and the y-intercept is unchanged.
C. The slope is unchanged and the y-intercept is shifted down 4
units.
D. The slope is multiplied by - 2/3, and the y-intercept is shifted
down 4 units.
$200 Answer from Linear
Functions
D
$300 - Linear Functions
Write then graph a linear equation that
includes the points (2, -1) and (-1, -4).
$300 - Linear Functions
y=x–3
$400 - Linear Functions
Determine the input when the output of
the linear function below is zero.
x
f(x)
-2
10
1
4
4
-2
$400 - Linear Functions
f(3) = 0.
$500 - Linear Functions
To build the perfect scale model of the SR-71 Blackbird Jet, it
is best to use the ratio of 3:4 to compare inches of the model to
feet of the plane. Which equation shows this ratio, if p is the
length of the plane in feet and m is inches of the model.
A. 12p = m
B. 12m = p
$500 - Linear Functions
C
$100 - Linear Equations and
Inequalities
Which ordered pair is not a solution to the
linear inequality -3x + 2y > -6?
A.
B.
C.
D.
(0, -2)
(0, 2)
(2, 0)
(0, 0)
$100 Answer from Linear Equations
and Inequalities
C
$200 - Linear Equations and
Inequalities
Which inequality best corresponds to the graph?
A. x + y ≥ 3.5
B. x - y ≥ -3.5
C. x + y ≤ 3.5
D. x - y ≤ 3.5
$200 Answer - Linear Equations and
Inequalities
B. x - y ≥ -3.5
$300 - Linear Equations and
Inequalities
You pull out the plug from the bathtub. After 40 seconds, there
are 13 gallons of water left in the tub. One minute after you
pull the plug, there are 10 gallons left. Assume that the
number of gallons varies linearly with the time since the plug
was pulled.
Find the y-intercept (gallon-intercept). What does this number
represent in the real world?
Find the x-intercept (time- intercept). What does this number
represent in the real world?
$300 - Linear Equations and
Inequalities
The equation to represent this problem is
The y-intercept is (0,19). This represents how much water
started out in the tub.
The x-intercept is (126.66…, 0). This represents how many
seconds it takes to drain the entire tub.
$400 - Linear Equations and
Inequalities
The velocity of an object fired directly
upward is given by V = 80 – 32t,
where t is in seconds. When will the
velocity be between 32 and 64 feet per
second?
$400 - Linear Equations and
Inequalities
32 < 80 – 32t < 64
32 – 80 < 80 – 80 – 32t < 64 – 80
–48 < –32t < –16
–48
/ –32 > –32t / –32 > –16 / –32
1.5 > t > 0.5
$500 - Linear Equations and
Inequalities
Compare the graph and function
below. Which has a greater
maximum? How do you know?
$500 - Linear Equations and
Inequalities
Has a vertex at (-2, 19) therefore has
a higher maximum.
The graph has a vertex of about (2.5, 3)
therefore has a lower maximum
$100 - Non-Linear Functions
Which of the following tables represents a
quadratic function?
A.
B.
C.
D.
x
y
x
y
x
y
x
y
3
3
2
2
-12
24
8
4
9
1
4
4
1
-2
6
6
18
.5
8
8
8
-16
4
4
54
1
10
10
-4
8
2
-2
$100 - Non-Linear Functions
D.
x
y
8
4
6
6
4
4
2
-2
x
f(x) =
$200 - Non-Linear Functions
Which of these is a reasonable equation for the graph?
A. f(x) = 0.5x
B. f(x) = 0.5x2
C. f(x) = 2x2 + 2
D. f(x) = 2x + 5
$200 - Non-Linear Functions
B. f(x) = 0.5x2
$300 - Non-Linear Functions
Which of the following tables represents exponential data?
A.
B.
C.
D.
x
-2
y
5
x
2
y
0.5
x
-2
y
8
x
-2
y
12
-1
4
4
0.7
-1
4
-1
15
0
3
4
1.5
0
2
0
16
1
2
8
5
1
1
1
15
$300 - Non-Linear Functions
C.
x
-2
y
8
-1
4
0
2
1
1
$400 -Non-Linear Functions
Listed below are several statements about the solutions of this
equation:
x2 + 4x – 12 = 0.
Which of the following statements is not true?
A. The solutions to the equation are -6 or 2.
B. The y-intercept is the solution to the equation.
C. The graph of y = x2 + 4x – 12 has two x-intercepts.
D. The graph of y = x2 + 4x – 12 has one y-intercepts.
$400 – Non-Linear Functions
B. The y-intercept is the solution to the equation.
$500 - Non-Linear Functions
State how you know the
difference between a
linear, exponential or
quadratic function when
given a set of points.
$500 - Non-Linear Functions
Linear – constant change
Exponential – common ratio
Quadratic – common second difference
Final Jeopardy
What are the domain and
range for the function f(x)
= -x2 -1?
Final Jeopardy Answer
D: all real numbers
R: y ≤ -1