Question 1

The circumference of a circle is given by  where r is the radius of the circle. What is the circumference of a circle with a 5-in. radius?

Accepted Answer

Substitute r = 5 in the given formula:
Circumference = 2πr = 2π(5) = 10π = 11eaa8b1_dcba_5ce1_b1b6_371a9280db0f_TB6026_11. Therefore, the correct option is C.

Question 2

Use the vertical-line test to determine whether the graph represents y as a function of x.

Accepted Answer

The vertical-line test states that if a vertical line can intersect the graph at more than one point, then the graph does not represent a function. Looking at the given graph, it is clear that any vertical line can intersect the graph at most only once, which means that the graph represents y as a function of x. Therefore, the correct option is B.

Question 3

Determine whether the statement is true or false. If f is a function, then f (a + b) = f (a) + f (b).

Accepted Answer

The statement is known as the Cauchy functional equation and not all functions satisfy it. For example, any function of the form f(x) = cx (where c is a constant) does satisfy the equation, but some non-linear functions like f(x) = x^2 do not satisfy the equation. Therefore, the statement is false in general.

Question 4

Let f be the function defined by f (x) = 8x + 9. Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

Accepted Answer

The answer of Let f be the function defined by...

Question 5

Find the domain of the function

Accepted Answer

The answer of Find the domain of the function ...

Question 6

The following graph shows the ratio of bachelor's degrees earned by women to men from 1960 through 1990. How fast was the ratio changing in the period from 1960 to 1980? From 1980 to 1990?

Accepted Answer

The answer of The following graph shows the ratio of...

Question 7

In a certain state, the sales tax T on the amount of taxable goods is 1% of the value of the goods purchased (x), where both T and x are measured in dollars. Express T as a function of x.

Accepted Answer

The question gives the formula for the sales tax as T=0.01x. This means that the sales tax is a function of the value of the goods purchased (x) and that it is equivalent to 1% of x. Therefore, the correct answer is option D, T(x) = 0.01x.

Question 8

The surface area S of a single-celled organism may be found by multiplying 4p times the square of the radius r of the cell. Express S as a function of r.

Accepted Answer

The answer of The surface area S of a single-celled...

Question 9

Refer to the graph of the function f in the following figure.  Find the value of x for which f (x) = 2 and f (x) = 0.

Accepted Answer

The answer of Refer to the graph of the function...

Question 10

Find the domain of the function.

Accepted Answer

The answer of Find the domain of the function. 
...

Question 11

Determine the domain of the given equation.

Accepted Answer

The answer of Determine the domain of the given equation....

Question 12

The volume of a spherical cancerous tumor is given by the function  where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is quintuple?

Accepted Answer

The answer of The volume of a spherical cancerous tumor...

Question 13

Find the domain of the function.

Accepted Answer

The answer of Find the domain of the function. 
...

Question 14

Ace Truck leases its 10-ft box truck at $25/day and $0.45/mi, whereas Acme Truck leases a similar truck at $20/day and $0.55/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

Accepted Answer

The daily cost for Ace Truck is $25 plus $0.45 per mile, which is represented by 25 + 0.45x. For Acme Truck, the cost is $20 plus $0.55 per mile, represented by 20 + 0.55x.

Question 15

The volume of a spherical cancerous tumor is given by the function  where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is decuple?

Accepted Answer

The answer of The volume of a spherical cancerous tumor...

Question 16

Let f be the function defined by
  Find f (0), f (4), and f (8).  __________  __________  __________

Accepted Answer

The answer of Let f be the function defined by
...

Question 17

Find the domain of the function  Give the answer as an interval or union of intervals.

Accepted Answer

The answer of Find the domain of the function ...

Question 18

Let f be the function defined by f (x) = 7x + 8. Find     and

Accepted Answer

The answer of Let f be the function defined by...

Question 19

Let f be the function defined by  Find    and   = __________  = __________  = __________  = __________

Accepted Answer

The answer of Let f be the function defined by...

Question 20

Find the range of the function.

Accepted Answer

The answer of Find the range of the function. 
...

Quiz 2: Functions, Limits and the Derivative

The circumference of a circle is given by where r is the radius of the circle. What is the circumference of a circle with a 5-in. radius?

Use the vertical-line test to determine whether the graph represents y as a function of x.

Determine whether the statement is true or false. If f is a function, then f (a + b) = f (a) + f (b) .

Let f be the function defined by f (x) = 8x + 9. Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

Find the domain of the function

The following graph shows the ratio of bachelor's degrees earned by women to men from 1960 through 1990. How fast was the ratio changing in the period from 1960 to 1980? From 1980 to 1990?

In a certain state, the sales tax T on the amount of taxable goods is 1% of the value of the goods purchased (x) , where both T and x are measured in dollars. Express T as a function of x.

The surface area S of a single-celled organism may be found by multiplying 4p times the square of the radius r of the cell. Express S as a function of r.

Refer to the graph of the function f in the following figure. Find the value of x for which f (x) = 2 and f (x) = 0.

Find the domain of the function.

Determine the domain of the given equation.

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is quintuple?

Find the domain of the function.

Ace Truck leases its 10-ft box truck at $25/day and $0.45/mi, whereas Acme Truck leases a similar truck at $20/day and $0.55/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is decuple?

Let f be the function defined by Find f (0), f (4), and f (8). __

Find the domain of the function Give the answer as an interval or union of intervals.

Let f be the function defined by f (x) = 7x + 8. Find and

Let f be the function defined by Find and = = = =

Find the range of the function.

Quiz 2: Functions, Limits and the Derivative

The circumference of a circle is given by where r is the radius of the circle. What is the circumference of a circle with a 5-in. radius?

Use the vertical-line test to determine whether the graph represents y as a function of x.

Determine whether the statement is true or false. If f is a function, then f (a + b) = f (a) + f (b) .

Let f be the function defined by f (x) = 8x + 9. Find f (5), f (- 5), f (a), f (- a), and f (a + 5).

Find the domain of the function

The following graph shows the ratio of bachelor's degrees earned by women to men from 1960 through 1990. How fast was the ratio changing in the period from 1960 to 1980? From 1980 to 1990?

In a certain state, the sales tax T on the amount of taxable goods is 1% of the value of the goods purchased (x) , where both T and x are measured in dollars. Express T as a function of x.

The surface area S of a single-celled organism may be found by multiplying 4p times the square of the radius r of the cell. Express S as a function of r.

Refer to the graph of the function f in the following figure. Find the value of x for which f (x) = 2 and f (x) = 0.

Find the domain of the function.

Determine the domain of the given equation.

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is quintuple?

Find the domain of the function.

Ace Truck leases its 10-ft box truck at $25/day and $0.45/mi, whereas Acme Truck leases a similar truck at $20/day and $0.55/mi. Find the daily cost of leasing from each company as a function of x number of miles driven.

The volume of a spherical cancerous tumor is given by the function where r is the radius of the tumor in centimeters. By what factor is the volume of the tumor increased if its radius is decuple?

Let f be the function defined by Find f (0), f (4), and f (8). __________ __________ __________

Find the domain of the function Give the answer as an interval or union of intervals.

Let f be the function defined by f (x) = 7x + 8. Find and

Let f be the function defined by Find and = __________ = __________ = __________ = __________

Find the range of the function.

Let f be the function defined by Find f (0), f (4), and f (8). __

Let f be the function defined by Find and = = = =