chamblee middle schoolchambleems.dekalb.k12.ga.us/downloads/iv-t20-observe... · 2016-04-05 ·...

4/3/2016 USATestprep, Inc.

http://www.usatestprep.com/modules/quiz_factory/qf.php?testid=535 1/13

Coordinate Algebra EOC (GSE) Quiz Answer KeyFunctions - (MGSE9‐12.F.LE.3 ) Observe Using Graphs

Student Name: _______________________ Date: _________Teacher Name: THUYNGA DAO Score: _________

1)

Which graph grows the fastest?

A) black

B) blue

C) green

D) pink

Explanation:The green function is an exponential function and it grows biggest the fastest.

2) Make a t-table for each function for the x-values 2 to 6. Which graph grows the fastest?

A) y = 2x

B) y = x3

C) y = 3x

D) y = x + 3

Explanation:

y = 3x is an exponential function. When you make your t-table, the value when x = 6 is largest on the exponential function.

3)

The table on the left is that of a linear function, and the one on the right is that of an exponential function.



Can you tell which function has the higher rate of growth? How?

A) There is not enough information to make a conclusion.

B) The linear function is growing faster, because at x = 3 the y-value of the linear function is larger.

C) The exponential function is growing faster, because at x = 0 the y-value of the exponential function is larger.

D)The exponential function is growing faster, because it grows by a factor that is multiplied by the previous y-value insteadof being added like the linear function.

Explanation:The exponential function grows faster because it grows by a factor that is multiplied by the previous y-value instead of being addedlike the linear function..

4)

blue: quadratic

green: exponential

pink: cubic

black: linear

Which function is growing the fastest?

A) cubic

B) exponential

C) linear

D) quadratic

Explanation:The exponential is growing the fastest. It is getting taller quickest.



5) Make a t-table for each function for the x-values 2 through 6. Which function grows the fastest?

A) y = x

B) y = x2

C) y = x3

D) y = 4x

Explanation:

y = 4x is an exponential function and therefore it grows the fastest.

6)

Blue: y = 7x

Pink: y = 5x3

Black: y = 4x2

Green: y = 3x

As x gets very large, which function becomes largest and remains so?

A) y = 7x

B) y = 5x3

C) y = 4x2

D) y = 3x

Explanation:

Since y = 3x is an exponential function, it grows the fastest and becomes exponentially larger as x approaches infinity.

7) Sarah is trying to convince her friend Brianna that the exponential function f(x) = 2x will eventually grow larger than the

polynomial function g(x) = x30. When Brianna plugs in 5 for x and sees that f(5) = 25 = 32, while g(5) = 530 = 9.3 x 1020, she is reallyconvinced that f will never be larger than g.

Which of these is the smallest value of x that Sarah can use to prove that f will grow larger than g?

A) 10

B) 100

C) 1000

D) 10000

Explanation:

1000 is correct. Note that f(1000) = 21000 = (24)250 = 16250, which is larger than g(1000) = 100030 = (103)30 = 1090.

8) Let f(x) = x100 and g(x) = 2x.

As x → ∞, which statement is true?

A) f(x) > g(x)

B) g(x) > f(x)

C) f(x) = g(x)



D) Insufficient information.

Explanation:g(x) > f(x) is correct. Any exponential function will eventually grow larger than any polynomial function, even if the degree is very

large. Note that f(10000) = 10000100 = 10400, while g(10000) = 210000 = (25)4000 = 324000.



9)

The graph shows two functions: a polynomial, y = f(x), and an exponential, y = g(x). Which statement about the functions is true?

A) as x→ ∞, f(x) < g(x)

B) as x→ ∞, f(x) = g(x)

C) as x→ ∞, f(x) > g(x)

D) None of the statements are true.

Explanation:From the graph you can see that both functions are increasing. If you zoomed out you would find that the rate of change for theexponential is larger than the polynomial so as x→ ∞, f(x) < g(x)

10) Which quantity is larger?

A) 100500

B) 1000300

C) They are equal.

D) Insufficient information.

Explanation:

100500 is correct. Since 100500 = (102)500 = 101000. But 1000300 = (103)300 = 10900.

11)



Jana has to solve a system of equations that contains an exponential function and a linear function. She decides to solve graphicallyand the graph she obtained is shown.

Is the complete solution shown? Why or why not?

A) Yes, since one of the equations is linear the two functions can only intersect once and the intersection point is shown.

B)Yes, since the slope of the line is not as great as the rate of change of the exponential the y-values will be greater andthey will only intersect one time.

C)No, exponential functions are the fastest growing functions. Since this is decay, eventually the exponential will level outwhere as the line has a constant rate of change. Therefore the exponential will eventually have higher y-values than theline. There must be a second intersection point.

D)No, even though the line has a smaller rate of change initially than the exponential, eventually the exponential will haveto have a smaller rate of change than the linear since they are the fastest growing functions. Given that there must be atleast one more intersection point somewhere near y = -1.

Explanation:No, exponential functions are the fastest growing functions. Since this is decay, eventually the exponential will level out where asthe line has a constant rate of change. Therefore the exponential will eventually have higher y-values than the line. There must be asecond intersection point.

Exponentials will eventually exceed all other functions as they are the fastest growing functions.



12)

The graph shows four functions:

y = 50x in black

y = 10x2 in green

y = x3 - 5

y = (1.25)x

Which function will have the largest value as x → ∞?

A) y = 50x

B) y = 10x2

C) y = x3 - 5

D) y = (1.25)x

Explanation:The functions are linear, quadratic, cubic and exponential. from looking at the graph it might seem like the linear will have the

largest y-values but as x gets larger and larger the exponential function will grow the fastest. Therefore y = 1.25x will have thelargest value as x &arr; ∞

13)

Comparing four Functions

x-values A (linear) B (quadratic) C (quartic) D (exponential)

1 50 10 1 1.25

10 500 1000 10,000 9.313

20 1000 4000 160,000 86.736

30 1500 9000 810,000 807.794

40 2000 16000 2,560,000 7523.16

The table shows values for four functions evaluated at the same x-values. Which function will have the largest value as x → ∞?

{The functions are labeled A, B, C, and D in the columns.]

A)

B)

C)

D)

Explanation:The exponential function will. Even though it does not have the largest y-value for the largest x-value shown you an see from the



table that it has the greatest rate of change. Therefore, as x gets larger and larger the y-vlaues of the exponential will overtake theother functions.



14)

x y = x2 + 200 y = 2x - 2 y = 3x2 + 6 y = x8

1 201 0 9 1

2 204 2 18 256

3 209 6 33 6,561

Compare the functions in the table. As the value of x increases, which function will eventually exceed the value of the otherfunctions?

A) y = x8

B) y = 2x - 2

C) y = 3x2 + 6

D) y = x2 + 200

Explanation:

y = 2x - 2

Any exponential function with a base greater than 1 will eventually exceed any polynomial function.

15)

Jana has to solve a system of equations that contains an exponential function and a linear function. She decides to solve graphicallyand the graph she obtained is shown.

Is the complete solution shown? Why or why not?

A) Yes, since one of the equations is linear the two functions can only intersect once and the intersection point is shown.

B)Yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will onlyintersect one time.

C)No, exponential functions are the fastest growing functions so eventually it will overpower the line. There must be asecond intersection point.

D)No, even though the line has a greater rate of change and will eventually have greater y-values, the exponential musthave greater y-values at some point. There must be at least three intersection points.



Explanation:No, exponential functions are the fastest growing functions so eventually it will overpower the line. There must be a secondintersection point.

Exponentials will eventually exceed all other functions as they are the fastest growing functions.



16)

x y = x10 y = 10x

1 1 10

2 1,024 100

3 59,049 1,000

4 1,048,576 10,000

Compare the two functions in the table. Will the value of function y = 10x eventually exceed the value of function y = x10?

A) No, any polynomial function will eventually exceed any exponential function with a base greater than 1.

B) No, any exponential function with a base greater than 1 will eventually exceed any polynomial function.

C) Yes, any polynomial function will eventually exceed any exponential function with a base greater than 1.

D) Yes, any exponential function with a base greater than 1 will eventually exceed any polynomial function.

Explanation:Yes, any exponential function with a base greater than 1 will eventually exceed any polynomial function.

17)

x y = 5x4 + 100 y = x3 + x2 y = x5 y = 3x

1 105 2 1 3

2 180 12 32 9

3 505 36 243 27


A) y = x5

B) y = 3x

C) y = x3 + x2

D) y = 5x4 + 100

Explanation:

y = 3x




18)

x y = 1000x3 + 1 y = 3x3 + 10 y = 5x y = x5

1 1,001 13 5 1

2 8,001 91 25 32

3 27,001 202 125 243


A) y = 5x

B) y = x5

C) y = 3x3 + 10

D) y = 1000x3 + 1

Explanation:

y = 5x


19) Eloise had to solve a system of inequalities that contained an exponential growth function and a linear function with positiveslope.

She KNOWS that the two equations intersect at least once, and she was asked to state the interval where the linear > exponential.

Which could be an answer to her system of inequalities?

A) (-1, 3)

B) (-1, ∞)

C) (-∞, -1)

D) (-&infin, -1) ∪ (3, ∞)

Explanation:If the line and the exponential function intersect only once then the line is tangent to the exponential at that point and therefore isalways below the exponential except at the point of intersection where they are equal.

Since they intersect at least once the only other option is they intersect twice where the line is above the exponential between thetwo intersection points. This is because exponentials will eventually exceed all other functions as they are the fastest growingfunctions.

Therefore, the only viable answer is (-1, 3)



20)

x y = 1.01x y = x2 y = 100x3 y = x6 + 10x

1 1.01 1 100 11

2 1.02 4 800 84

3 1.03 9 2,7000 759


A) y = x2

B) y = 100x3

C) y = 1.01x

D) y = x6 + 10x

Explanation:

y = 1.01x


21)

x y = x10 y = 2x

1 1 2

2 1,024 4

3 59,049 8

4 1,048,576 16

Compare the two functions in the table. Will the value of function y = 2x eventually exceed the value of function y = x10?

A) No, any polynomial function will eventually exceed any exponential function with a base greater than 1.

B) No, any exponential function with a base greater than 1 will eventually exceed any polynomial function.

C) Yes, any polynomial function will eventually exceed any exponential function with a base greater than 1.

D) Yes, any exponential function with a base greater than 1 will eventually exceed any polynomial function.

Explanation:Yes, any exponential function with a base greater than 1 will eventually exceed any polynomial function.

chamblee middle schoolchambleems.dekalb.k12.ga.us/downloads/iv-t20-observe... · 2016-04-05 ·...

Documents