Quiz about Defining, Comparing, Identifying Functions

Question 1

The table below represents the function F. The equation that represents this function is

Accepted Answer

F(x) = 2^x + 1

Answer

F(x) = 3x

Answer

F(x) = 3x

Answer

F(x) = 2x + 3

Question 2

If f(x)=3^x and g(x)= 2x + 5, at which value of x is f(x) < g(x) ?

Accepted Answer

-1

Answer

2

Answer

-3

Answer

4

Question 3

The graph of the equation y=ax² is shown below.

Accepted Answer

wider and opens downward

Answer

wider and opens upward

Answer

narrower and opens downward

Answer

narrower and opens upward

Question 4

The table below shows the average yearly balance in a savings account where interest is compounded annually. No money is deposited or withdrawn after the initial amount is deposited.

Which type of function best models the given data?

Accepted Answer

exponential growth function

Answer

linear function with negative rate of change

Answer

linear function with positive rate of change

Answer

exponential decay function

Question 5

Krystal was given $3000 when she turned 2 years old. Her parents invested it at a 2% interest rate compounded annually. No deposits or withdrawals were made. Which expressions can be used to determine how much money Krystal had in the account when she turned 18?

Accepted Answer

3000(1 + 0.02)¹⁶

Answer

3000(1 - 0.02)¹⁶

Answer

3000(1 + 0.02)¹⁸

Answer

3000(1 - 0.02)¹⁸

Question 6

Mario's $15,000 car depreciates in value at a rate of 19% per year. The value, V, after t years can be modeled by the function V = 15,000(0.81)^t. Which function is equivalent to the original function?

Accepted Answer

V = 15,000(0.9)^2t

Answer

V = 15,000(0.9)^9t

Answer

V = 15,000(0.9)^t/9

Answer

V = 15,000(0.9)^t/2

Question 7

The function V(t) =1350(1.017)^t represents the value V(t), in dollars, of a comic book t years after its purchase. The yearly rate of appreciation of the comic book is

Accepted Answer

1.7%

Answer

17%

Answer

1.017%

Answer

0.017%

Question 8

The equation A= 1300(1.02)⁷ is being used to calculate the amount of money in a savings account. What does 1.02 represent in this equation?

Accepted Answer

2% growth

Answer

0.02% decay

Answer

0.02% growth

Answer

2% decay

Question 9

Which table of values represents a linear relationship?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 10

The value in dollars, v(x), of a certain car after x years is represented by the equation v(x) = 25,000(0.86)^x. To the nearest dollar, how much more is the car worth after 2 years than after 3 years?

Accepted Answer

2589

Answer

6510

Answer

15,901

Answer

18,490

Question 11

Miriam and Jessica are growing bacteria in a laboratory. Miriam uses the growth function f(t) = n^2t while Jessica uses the function g(t) = n^4t, where n represents the initial number of bacteria and t is the time, in hours. If Miriam starts with 16 bacteria, how many bacteria should Jessica start with to achieve the same growth over time?

Accepted Answer

4

Answer

32

Answer

16

Answer

8

Question 12

The country of Benin in West Africa has a population of 9.05 million people. The population is growing at a rate of 3.15 each year. Which function can be used to find the population 7 years from now?

Accepted Answer

f(t) = (9.05 x 10⁶)( 1+ 0.031)⁷

Answer

f(t) = (9.05 x 10⁶)(1 - 0.31)⁷

Answer

f(t) = (9.05 x 10⁶)(1 + 0.31)⁷

Answer

f(t) = (9.05 x 10⁶)(1 - 0.031)⁷

Question 13

For a recently released movie, the function y = 119.67(0.61)^x models the revenue earned, y, in millions of dollars each week, x, for several weeks after its release.

Based on the equation, how much more money, in millions of dollars, was earned in revenue for week 3 than for week 5?

Accepted Answer

17.06

Answer

37.27

Answer

27.16

Answer

10.11

Question 14

If a population of cells triples every hour, which function represents p(t), the population after t hours?

Accepted Answer

p(t) = 100(3)^t

Answer

p(t) = 3(100)^t

Answer

p(t) = 3t +100

Answer

p(t) = 100t + 3

Question 15

The highest possible grade for a book report is 100. The teacher deducts 10 points for each day the report is late.

Accepted Answer

Linear

Answer

Quadratic

Answer

Exponential Growth

Answer

Exponential Deccay

Question 16

Tables below show the values of four different functions for given values of x.

Which table represents a linear function?

Accepted Answer

f(x)

Answer

g(x)

Answer

h(x)

Answer

k(x)

Question 17

A student invest $500 for 3 years in a savings account that earns 4% interest per year. No further deposits or withdrawals are made during this time. Which statement does not yield the correct balance in the account at the end of 3 years?

Accepted Answer

500(1 - .04)³

Answer

500(1.04)³

Answer

500(1 + .04)(1 + .04)(1 + .04)

Answer

500 + 500(.04) + 520(.04) + 540.8(.04)

Question 18

Milton has his money invested in a stock portfolio. The value, v(x), of his portfolio can be modeled with the function v(x) = 30,000(0.78)^x, where x is the number of years since he made his investment. Which statement describes the rate of change of the value of his portfolio?

Accepted Answer

It decreases 22% per year.

Answer

It decreases 78% per year.

Answer

It increases 78% per year.

Answer

It increase 22% per year.

Question 19

Which scenario represents exponential growth?

Accepted Answer

A species of fly doubles its population every month during the summer.

Answer

A water tank filled at a rate of 2 gallons/minute.

Answer

A vine grows 6 inch every week.

Answer

A car increases its distance from a garage as it travels at a constant speed of 25 miles per hour.

Question 20

Anne invested $1000 in an account with a 1.3% annual interest rate. She made no deposits or withdrawals on the account for 2 years. If interest was compounded annually, which equation represents the balance in the account after the 2 years?

Accepted Answer

A = 1000(1 + 0.013)²

Answer

A = 1000(1 - 0.013)²

Answer

A = 1000(1 - 1.3)²

Answer

A = 1000(1 + 1.3)²

Question 21

The graph below represents a jogger's speed during her 20-minute jog around her neighborhood.

Which statement best describes what the jogger was doing during the 9 - 12 minute interval of her jog?

Accepted Answer

She was jogging at a constant rate.

Answer

She was standing still.

Answer

She was increasing her speed.

Answer

She was decreasing her speed.

Question 22

To keep track of his profits, the owner of a carnival booth decided to model his ticket sales on a graph. He found that his profits only declined when he sold between 10 and 40 tickets. Which graph could represent his profits?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 23

A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population growth?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 24

The table below represents the function F.

The equation that represents this function is

Accepted Answer

F(x) = 2^x + 1

Answer

F(x) = 3^x

Answer

F(x) = 3x

Answer

F(x) = 2x + 3

Question 25

If f(x) = 1/3 x + 9, which statement is always true?

Accepted Answer

If x > 0, then f(x) > 0

Answer

f(x) < 0

Answer

f(x) > 0

Answer

If x < 0, then f(x) < 0

Question 26

Which point is not on the graph represent by y = x² +3x - 6?

Accepted Answer

(3, -6)

Answer

(-6, 12)

Answer

(-4, -2)

Answer

(2, 4)

Question 27

The graph of y = f(x) is shown below.

Which point could be used to find f(2)?

Accepted Answer

A

Answer

B

Answer

C

Answer

D

Question 28

If f(x) = 3^x and g(x) = 2x + 5, at which value of x is f(x) < g(x) ?

Accepted Answer

-1

Answer

2

Answer

-3

Answer

4

Question 29

Which equation(s) represent the graph below?

I. y = (x + 2)(x² - 4x - 12)

II. y = (x - 3)(x² + x - 2)

III. y = (x - 1)(x² - 5x - 6)

Accepted Answer

II and III

Answer

I, only

Answer

II, only

Answer

I and II

Question 30

A laboratory technician studied the population growth of a colony of bacteria. He recorded the number of bacteria every other day, as shown in the partial table below.

Which function would accurately model the technician's data?

Accepted Answer

f(t) = 25^t-1

Answer

f(t) = 25^t

Answer

f(t) = 25t

Answer

f(t) = 25(t + 1)

Question 31

Which function is shown in the table below?

Accepted Answer

f(x) = 3^x

Answer

f(x) = 3x

Answer

f(x) = x + 3

Answer

f(x) = -x³

Question 32

The graph of f(x) is shown below.

Which function could represent the graph of f(x)?

Accepted Answer

f(x) = (x + 2)(x² + 3x - 4)

Answer

f(x) = (x - 2)(x² + 3x - 4)`

Answer

f(x) = (x + 2)(x² + 3x + 4)

Answer

f(x) = (x - 2)(x² + 3x + 4)

Question 33

What is the largest integer, x, for which the value of f(x) = 5x⁴ + 30x² + 9 will be greater than the value of g(x) = 3^x?

Accepted Answer

10

Answer

7

Answer

8

Answer

9

Question 34

Which chart could represent the function f(x) = -2x + 6?

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 35

As x increase beyond 25, which function will have the largest value?

Accepted Answer

f(x) = 1.5^x

Answer

g(x) = 1.5x + 3

Answer

h(x) = 1.5x²

Answer

k(x) = 1.5x³ + 1.5x²

Question 36

Lynn, Jude, and Anne were given the function f(x) = -2x² + 32, and they were asked to find f(3). Lynn's answer was 14, Jude's answer was 4, and Anne's answer was +/- 4. Who is correct?

Accepted Answer

Lynn, only

Answer

Jude, only

Answer

Anne, only

Answer

Both Lynn and Jude

Question 37

Wenona sketched the polynomial P(x) as shown on the axes below. Which equation could represent P(x)?

Accepted Answer

P(x) = (x + 10(x - 2)²

Answer

P(x) = (x - 1)(x + 2)²

Answer

P(x) = (x + 1)(x - 2)

Answer

P(x) = (x - 1)(x + 2)

Question 38

In a sequence, the first term is 3 and the common difference is 2. The fifth term of this sequence is

Accepted Answer

11

Answer

-5

Answer

-3

Answer

9

Question 39

The third term in an arithmetic sequence is 11 and the fifth term is 27. If the first term is a₁, which is an equation for the nth term of this sequence?

Accepted Answer

a_n = 8n - 13

Answer

a_n = 8n + 11

Answer

a_n = 16n + 11

Answer

a_n= 16n - 37

Question 40

Which function defines the sequence -6, -10, -14, -18, ..., where f(6) = -26 ?

Accepted Answer

f(x) = - 4x - 2

Answer

f(x) = 4x - 2

Answer

f(x) = - x + 32

Answer

f(x) = x - 26

Question 41

What is the domain of the relation shown below?

{(4,2), (1,1), (0,0), (1, -1), (4,-2)}

Accepted Answer

{0, 1, 4}

Answer

{-2, -1, 0, 1, 2}

Answer

{-2, -1, 0, 1, 2, 4}

Answer

{-2, -1, 0, 0, 1, 1, 1, 2, 4, 4}

Question 42

Which table represents a function?

Accepted Answer

Option C is correct

Answer

A.

Answer

B.

Answer

D.

Question 43

The range of the function f(x) = x² + 2x - 8 is all real numbers

Accepted Answer

greater than or equal to -9

Answer

less than or equal to -9

Answer

less than or equal to -1

Answer

greater than or equal to -1

Question 44

A mapping is shown in the diagram below. This mapping is

Accepted Answer

not a function, because Feb has two outputs, 28 and 29

Answer

a function, because Feb has two outputs, 28 and 29

Answer

a function, because two inputs, Jan and Mar, result in the output 31

Answer

not a function, because two inputs, Jan and Mar, result in the output 31

Question 45

Which graph represents

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

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