Question 1

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.
-

Accepted Answer

a)On a long trip, distance from home increases with time.
b)20 miles per hour.
c)Good model if speed is constant for 8 hours.

Question 2

For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
-(hours worked, yearly wages)

Accepted Answer

Answers may vary.
a)The domain of the function is the amount of hours worked per week between 10
and 60 hours and the range is yearly wages (in thousands of dollars)from $15K to
$90K.
b)  c)The function should be roughly increasing. Typically the more hours someone
works, the more money they make. Any time over 40 hours, usually includes an
overtime wage which raises the overall yearly wages dramatically. However, many
people have a fixed salary regardless of how many hours they work, so this may not
represent an appropriate model.

Question 3

In the following situation, state whether two variables are related in a way that might be described by a function. If so,
identify the independent and dependent variables.
-You make a list of the titles of books in a public library and their copyright year.

Accepted Answer

The relationship between book titles and their copyright years does not describe a function because a single copyright year can correspond to multiple book titles, violating the definition of a function where each input should have a unique output.

Question 4

Plot and label the given points.
-$(1,6),(-4,-2)$

Accepted Answer

The answer of Plot and label the given points.
-$(1,6),(-4,-2)$

...

Question 5

In the following situation, state whether two variables are related in a way that might be described by a function. If so,
identify the independent and dependent variables.
-You are taking a road trip in a car and want to know how far you've traveled (read the odometer) at various times during your trip.

Accepted Answer

In this scenario, time is the independent variable because it is the input or the variable you control. The distance traveled is the dependent variable because it depends on the amount of time passed. As time increases, the distance traveled changes accordingly, which can be described by a function.

Question 6

Plot and label the given points.
-$(5,-4),(-2,3)$

Accepted Answer

The answer of Plot and label the given points.
-$(5,-4),(-2,3)$

...

Question 7

Write the word or phrase that best completes each statement or answers the question.For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
-(size of truck, average fuel mileage)

Accepted Answer

The answer of Write the word or phrase that best...

Question 8

Plot and label the given points.
-The rate of change is equal to the slope of the graph.

Accepted Answer

The rate of change in a graph represents how one variable changes in relation to another, which is exactly what the slope of a graph indicates.

Question 9

Plot and label the given points.
-$( 0,6 ) , ( 0,1 )$

Accepted Answer

The answer of Plot and label the given points.
-\(( 0,6...

Question 10

Plot and label the given points.
-The population of a town with an initial population of 68,555 grows at a rate of 3.8% per year. Create an exponential function of the form Q 
$\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$

Accepted Answer

The correct exponential function for a population growing at a rate of 3.8% per year is $Q = 68,555 \times (1 + 0.038)^t$, which simplifies to $Q = 68,555 \times (1.038)^t$.

Question 11

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.
-

Accepted Answer

The answer of Briefly discuss the conditions under which a...

Question 12

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.
-

Accepted Answer

The answer of Briefly discuss the conditions under which a...

Question 13

Plot and label the given points.
-$(-4,-6),(-6,6)$

Accepted Answer

The answer of Plot and label the given points.
-$(-4,-6),(-6,6)$

...

Question 14

Plot and label the given points.
-$(5,6),(-1,4)$

Accepted Answer

The answer of Plot and label the given points.
-$(5,6),(-1,4)$

...

Question 15

Briefly discuss the conditions under which a linear function is a realistic model for the given situation.
-

Accepted Answer

The answer of Briefly discuss the conditions under which a...

Question 16

Provide an appropriate response.
-The following graph represents a function. Identify the independent and dependent variables and describe the domain and range.

Accepted Answer

The answer of Provide an appropriate response.
-The following graph represents...

Question 17

For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
-(time spent studying, percentage on exam)

Accepted Answer

The answer of For the given function:
a)Describe an appropriate domain...

Question 18

Write an equation for the linear function and use it to answer the given question.
-The Math Club plans to pay a visitor $62 to speak at a fundraiser. Tickets will be sold for $2 each. Find an equation that gives the profit/loss for the event as it varies with the number of tickets sold.
How many people must attend the event for the club to break even.

Accepted Answer

The profit equation is $p = -62 + 2n$, where $p$ is the profit and $n$ is the number of tickets sold. The club breaks even when profit is zero, so setting $p = 0$ gives $0 = -62 + 2n$, solving for $n$ gives $n = 31$.

Question 19

For the given function:
a)Describe an appropriate domain and range for the function.
b)Make a rough sketch of a graph of the function.
c)Briefly discuss the validity of your graph as a model of the true function.
-(miles ran per week, 5K time)

Accepted Answer

The answer of For the given function:
a)Describe an appropriate domain...

Question 20

Plot and label the given points.
-$(1,5),(3,-5)$

Accepted Answer

The answer of Plot and label the given points.
-$(1,5),(3,-5)$

...

Quiz 9: Modeling Our World

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

For the given function: a)Describe an appropriate domain and range for the function. b)Make a rough sketch of a graph of the function. c)Briefly discuss the validity of your graph as a model of the true function. -(hours worked, yearly wages)

In the following situation, state whether two variables are related in a way that might be described by a function. If so, identify the independent and dependent variables. -You make a list of the titles of books in a public library and their copyright year.

Plot and label the given points. - $(1,6),(-4,-2)$

Plot and label the given points. - $(5,-4),(-2,3)$

Plot and label the given points. -The rate of change is equal to the slope of the graph.

Plot and label the given points. - $( 0,6 ) , ( 0,1 )$

Plot and label the given points. -The population of a town with an initial population of 68,555 grows at a rate of 3.8% per year. Create an exponential function of the form Q $\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

Plot and label the given points. - $(-4,-6),(-6,6)$

Plot and label the given points. - $(5,6),(-1,4)$

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

Provide an appropriate response. -The following graph represents a function. Identify the independent and dependent variables and describe the domain and range.

For the given function: a)Describe an appropriate domain and range for the function. b)Make a rough sketch of a graph of the function. c)Briefly discuss the validity of your graph as a model of the true function. -(time spent studying, percentage on exam)

For the given function: a)Describe an appropriate domain and range for the function. b)Make a rough sketch of a graph of the function. c)Briefly discuss the validity of your graph as a model of the true function. -(miles ran per week, 5K time)

Plot and label the given points. - $(1,5),(3,-5)$

Quiz 9: Modeling Our World

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

For the given function: a)Describe an appropriate domain and range for the function. b)Make a rough sketch of a graph of the function. c)Briefly discuss the validity of your graph as a model of the true function. -(hours worked, yearly wages)

In the following situation, state whether two variables are related in a way that might be described by a function. If so, identify the independent and dependent variables. -You make a list of the titles of books in a public library and their copyright year.

Plot and label the given points. - (1,6),(−4,−2)(1,6),(-4,-2)(1,6),(−4,−2)

Plot and label the given points. - (5,−4),(−2,3)(5,-4),(-2,3)(5,−4),(−2,3)

Plot and label the given points. -The rate of change is equal to the slope of the graph.

Plot and label the given points. - (0,6),(0,1)( 0,6 ) , ( 0,1 )(0,6),(0,1)

Plot and label the given points. -The population of a town with an initial population of 68,555 grows at a rate of 3.8% per year. Create an exponential function of the form Q Q=Q0×(1+r) t\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }Q=Q0​×(1+r) t

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

Plot and label the given points. - (−4,−6),(−6,6)(-4,-6),(-6,6)(−4,−6),(−6,6)

Plot and label the given points. - (5,6),(−1,4)(5,6),(-1,4)(5,6),(−1,4)

Briefly discuss the conditions under which a linear function is a realistic model for the given situation. -

Provide an appropriate response. -The following graph represents a function. Identify the independent and dependent variables and describe the domain and range.

For the given function: a)Describe an appropriate domain and range for the function. b)Make a rough sketch of a graph of the function. c)Briefly discuss the validity of your graph as a model of the true function. -(time spent studying, percentage on exam)

For the given function: a)Describe an appropriate domain and range for the function. b)Make a rough sketch of a graph of the function. c)Briefly discuss the validity of your graph as a model of the true function. -(miles ran per week, 5K time)

Plot and label the given points. - (1,5),(3,−5)(1,5),(3,-5)(1,5),(3,−5)

Plot and label the given points. - $(1,6),(-4,-2)$

Plot and label the given points. - $(5,-4),(-2,3)$

Plot and label the given points. - $( 0,6 ) , ( 0,1 )$

Plot and label the given points. -The population of a town with an initial population of 68,555 grows at a rate of 3.8% per year. Create an exponential function of the form Q $\mathrm { Q } = \mathrm { Q } _ { 0 } \times ( 1 + \mathrm { r } ) ^ { \mathrm { t } }$

Plot and label the given points. - $(-4,-6),(-6,6)$

Plot and label the given points. - $(5,6),(-1,4)$

Plot and label the given points. - $(1,5),(3,-5)$