jeopardy - functions identifying functions function characteristics linear functions non-linear...

Jeopardy - functionsIdentifying Functions

Function

Characteristics

Linear Functions

Non-Linear Functions

Q $100

Q $200

Q $300

Q $400

Q $500

Q $100 Q $100Q $100 Q $100

Q $200 Q $200 Q $200 Q $200

Q $300 Q $300 Q $300 Q $300

Q $400 Q $400 Q $400 Q $400

Q $500 Q $500 Q $500 Q $500

Final Jeopardy

Linear Equations & Inequalities

$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


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.


Independent: videos rentedDependent: total costf(v) = 2.5v + 25


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.


Time(Hours)

Temp(˚F)

1 633 795 957 1119 127

11 146

y = 8x + 55


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? $2000

$1900

$1800

$1600

$800

2002 2003 2004 2005 2006

Computer Price


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

• Graph -2x + 4y = 4 for the domain D: {-8, -4, 0, 4, 8}


2 4 6 8–2–4–6–8 x

2

4

6

8

–2

–4

–6

–8

y

$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}


B. D: {x ≥ 0}; R: {y ≥ 0}


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


I, III, and IV


What is the value of the functionwhen the input is 2?

$400 Answer from Function Characteristics

f(2) = -3/4

$500 -Function CharacteristicsThe 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?

PositionValue of

term

1

2 6

3

4 24

5

n ?


C.

$100 - Linear FunctionsThe 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 FunctionsThe 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


Write then graph a linear equation that includes the points (2, -1) and (-1, -4).


y = x – 3


Determine the input when the output of the linear function below is zero.

x f(x)

-2 10

1 4

4 -2


f(3) = 0.

$500 - Linear FunctionsTo 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


C

$100 - Linear Equations and Inequalities

Which ordered pair is not a solution to the linear inequality -3x + 2y > -6?

A. (0, -2)B. (0, 2)C. (2, 0)D. (0, 0)

$100 Answer from Linear Equations and Inequalities

C


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


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?


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 manyseconds it takes to drain the entire tub.


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?


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


Compare the graph and function below. Which has a greater maximum? How do you know?


Has a vertex at (-2, 19) therefore hasa higher maximum.

The graph has a vertex of about (2.5, 3) therefore has a lower maximum

$100 - Non-Linear FunctionsWhich of the following tables represents a quadratic function?

x y

3 3

9 1

18 .5

54 1

x y

-12 24

1 -2

8 -16

-4 8

x y

2 2

4 4

8 8

10 10

x y

8 4

6 6

4 4

2 -2

A. B. C. D.

$100 - Non-Linear Functions

D. x y

8 4

6 6

4 4

2 -2

$200 - Non-Linear FunctionsWhich of these is a reasonable equation for the graph?

f(x) =

x

A. f(x) = 0.5x

B. f(x) = 0.5x2

C. f(x) = 2x2 + 2

D. f(x) = 2x + 5


B. f(x) = 0.5x2

$300 - Non-Linear FunctionsWhich of the following tables represents exponential data?

x y

-2 5

-1 4

0 3

1 2

x y

2 0.5

4 0.7

4 1.5

8 5

x y

-2 12

-1 15

0 16

1 15

x y

-2 8

-1 4

0 2

1 1

A. B. C. D.


x y

-2 8

-1 4

0 2

1 1

C.

$400 -Non-Linear FunctionsListed 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.


State how you know the difference between a linear, exponential or

quadratic function when given a set of points.


Linear – constant changeExponential – common ratioQuadratic – common second difference

Final Jeopardy

What are the domain and range for the function f(x) = -x2 -1?

Final Jeopardy Answer

D: all real numbersR: y ≤ -1

jeopardy - functions identifying functions function characteristics linear functions non-linear...

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