Quiz about Functions Comparing

Question 1

The table below shows some of the values for the linear function f.

Let g be the linear function defined by g(x) = 4x + 5.

Which statement is true?

Accepted Answer

The graph of g has a greater slope than the graph of f.

Answer

The graph of f has a greater slope than the graph of g.

Answer

The graph of f has the same slope as the graph of g.

Answer

The slopes of the graphs of f and g are undefined.

Question 2

Suppose a bacteria is introduced to two different solutions in separate petri dishes. The bacteria in the first solution grow at a rate modeled by the function G(t) = (1.40)^t. The bacteria in the second solution grow in accordance with the data displayed in the table. Which statement best describes the growth rates exhibited within the two different solutions?

Accepted Answer

The bacteria grow at a faster rate in the first solution.

Answer

The bacteria grow at the same rate in both solutions.

Answer

The bacteria grow at a slower rate in the first solution.

Answer

The bacteria decay in the first solution and grow in the second solution.

Question 3

Leonard compared the cost of purchasing a gallon of gas at two different gas stations. The function C(g) = 3.25 + 0.07x models the average cost of a gallon of gas at the first gas station after x months. The table below shows the average cost of a gallon of gas at the second gas station after different numbers of months. Which statement is true?

Accepted Answer

The second station had a higher initial price per gallon but increased at a smaller amount per month than the first station.

Answer

The first station had a higher initial price per gallon and increased at a greater amount per month than the second station.

Answer

The second station had a higher initial price per gallon and increased at a greater amount per month than the first station.

Answer

The first station had a higher initial price per gallon but increased at a smaller amount per month than the second station.

Question 4

Which statement below describes the comparison of rate of change between the linear function f(x) and the exponential function g(x).

Accepted Answer

g(x) will eventually exceed the rate of change of f(x).

Answer

g(x) rate of change is ALWAYS greater than f(x) rate of change.

Answer

g(x) is NEVER greater than f(x) rate of change.

Answer

There is not enough information to compare the rate of change of f(x) to g(x).

Question 5

These two incomplete tables are given to you, which function has a higher y value when x = 2? How much higher is this value?

Accepted Answer

Function B has a higher y-value when x = 2, it is 12 units higher

Answer

Function A has a higher y-value when x = 2, it is 12 units higher

Answer

Function B has a higher y-value when x = 2, it is 78 units higher

Answer

Function A has a higher y-value when x = 2, it is 4 units higher

Question 6

Which statement below describes the comparison of the linear function f(x) and the exponential function g(x)?

Accepted Answer

The value of g(x) will eventually exceed the value of f(x).

Answer

The value of g(x) is always greater than the value of f(x).

Answer

The value of g(x) is never greater than the value of f(x).

Answer

There is not enough information to compare the value of f(x) to the value of g(x).

Question 7

Accepted Answer

b

Answer

a

Answer

c

Answer

d

Question 8

Accepted Answer

b

Answer

a

Answer

c

Answer

d

Question 9

Two linear functions are shown. Linear function J is represented by the equation $$y=\frac{3}{4}x-6$$ . The table represents linear function K. Which Function has a larger x-intercept and what is its x-intercept?

Accepted Answer

Function J, 8

Answer

Function J, -6

Answer

Function K, 5

Answer

Function K, 10

Question 10

Two linear functions are shown below. Which function has the greater initial value?

Accepted Answer

Function A

Answer

Function B

Question 11

A lottery winner must choose between g(x) and h(x) for the distribution of winnings. Each month the distribution increases as shown in the tables. If the payout will last two years, which plan should the winner choose and why?

Accepted Answer

The winner should choose h(x) because it will eventually yield more money.

Answer

The winner should choose g(x) because the table starts with thousands.

Answer

g(x) will eventually yield more money than h(x).

Question 12

Which statement below is TRUE regarding the two functions?

Accepted Answer

Both functions have a y-intercept of 1

Answer

Both functions are linear

Answer

Both functions are increasing

Answer

Both functions are exponential growth

Question 13

Two linear functions are shown. Linear function J is represented by the equation $$y=\frac{3}{4}x-6$$ . The table represents linear function K. Which Function has a larger x-intercept and what is its x-intercept?

Accepted Answer

Function J, 8

Answer

Function J, -6

Answer

Function K, 5

Answer

Function K, 10

Question 14

The function f(x) = 14,000(1.3)^x models the population of of town 1 x years after January 2006. The table below shows the population of town 2 in different years. Assuming both towns continue to grow at the same rate, which statement is true?

Accepted Answer

Town 2 had a greater population than town 1 in 2006 and is growing at a faster rate than town 1.

Answer

Town 1 had a greater population than town 2 in 2006 and is growing at a faster rate than town 2.

Answer

Town 1 had a greater population than town 2 in 2006, but is growing at a slower rate than town 2.

Answer

Town 2 had a greater population than town 1 in 2006, but is growing at a slower rate than town 1.

Question 15

What is the approximate difference in the growth rates of the two functions?

Accepted Answer

5%

Answer

0%

Answer

3%

Answer

8%

Question 16

A scientist is observing the population of rabbits in two different areas of the state. -- The function f(x) = 9,620(0.84)^x models the population of rabbits in the western part of the state x years after the scientist began his observations. -- The table shows the population of rabbits in the eastern part of the state after different amounts of time. Which statement is true?

Accepted Answer

Both rabbit populations are changing in size at the same rate.

Answer

The eastern population of rabbits is changing in size at a faster rate than the western population.

Answer

Both rabbit populations had the same initial population.

Answer

The eastern population of rabbits had a greater initial population than the western population.

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