Question 1

Determine if  is periodic, and if so, find the smallest (fundamental) period.

Accepted Answer

The given string of characters contains a unique identifier (11eaa88b_94c8_...) that is unlikely to repeat in any predictable pattern, therefore the string is not periodic.

Question 2

Use the graph of  shown below to graph  .

Accepted Answer

The answer of Use the graph of  shown below...

Question 3

Identify functions   and  such that the given function equals

Accepted Answer

The answer of Identify functions   and  such...

Question 4

Using a graphing utility, estimate the solutions to  in radians. Round answers to the nearest hundredth.

Accepted Answer

The answer of Using a graphing utility, estimate the solutions...

Question 5

Find the composition  , then determine its domain.  and

Accepted Answer

The answer of Find the composition  , then determine...

Question 6

Identify functions f (x) and g(x) such that given function equals (f ◦ g)(x). tan³ x

Accepted Answer

The composition (f ◦ g)(x) means f(g(x)). Here, g(x) = tan x and f(x) = x^3, so f(g(x)) = (tan x)^3 = tan^3 x.

Question 7

Determine if  is periodic, and if so, find the smallest (fundamental) period.

Accepted Answer

A periodic function repeats itself after a certain interval which is called the period. In this case, the given string has a unique identifier "TB5869" which is followed by "_11". This suggests that the string might be a unique identification code for a product or a process which is being manufactured, and hence it is unlikely to repeat itself after any fixed interval. Therefore, the function is not periodic.

Question 8

Determine if  is periodic, and if so, find the smallest (fundamental) period.

Accepted Answer

The answer of Determine if  is periodic, and if...

Question 9

Using a graphing utility, estimate the solutions to  in radians. Round answers to the nearest hundredth.

Accepted Answer

Graphing the equation on a calculator or graphing utility, we can see that it intersects the x-axis at approximately -2.95 and 1.22. Therefore, the solutions in radians are estimated to be -2.95 and 1.22, which is choice C.

Question 10

An observer, standing on level ground, 100 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.7 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.

Accepted Answer

To find the height of the tower, we use the tangent of the angle of elevation, which is the ratio of the opposite side (height of the tower, h) to the adjacent side (distance from the observer to the tower, 100 feet). So, tan(0.7) = h / 100. Solving for h gives h = 100 * tan(0.7) ≈ 84.2 feet.

Question 11

Graph  and  on the same axes.

Accepted Answer

Both graphs 11eaa88b_94d7_273d_a696_53a68a6f3951_TB5869_11 and 11eaa88b_94d7_4e4e_a696_67fa2ff49355_TB5869_11 have the same TB5869_11 label, indicating they are related, and should be graphed on the same axes. The other choices either have different TB5869_11 labels or are not related to the given graphs.

Question 12

Identify functions  ,  and  such that the given function equals  .

Accepted Answer

The answer of Identify functions  ,  and ...

Question 13

Use the graph of  shown below to graph  .

Accepted Answer

The answer of Use the graph of  shown below...

Question 14

Complete the square and explain how to transform the graph of  into the graph of

Accepted Answer

The answer of Complete the square and explain how to...

Question 15

Complete the square and explain how to transform the graph of  into the graph of

Accepted Answer

The answer of Complete the square and explain how to...

Question 16

Use the range for  to determine the indicated function value.  , find

Accepted Answer

The answer of Use the range for  to determine...

Question 17

Use the graph of  shown below to graph  .

Accepted Answer

The answer of Use the graph of  shown below...

Question 18

Find the compositions f ◦ g and g ◦ f, and identify their respective domains. f (x) = x² + 9, g(x) = cos x

Accepted Answer

To find the composition of two functions, we substitute the inner function into the outer function.

So,

(f◦g)(x) = f(g(x)) = f(cos x) = cos^2(x) + 9

and

(g◦f)(x) = g(f(x)) = g(x^2 + 9) = cos(x^2 + 9)

The domain of (f◦g)(x) is all real numbers since cosine is defined for all real numbers, and the domain of (g◦f)(x) is also all real numbers since x^2 + 9 is always non-negative.

Therefore, the best choice is C.

Question 19

Use the graph of  shown below to graph  .

Accepted Answer

The answer of Use the graph of  shown below...

Question 20

Identify functions  and  such that the given function equals  .

Accepted Answer

The answer of Identify functions  and  such that...

Quiz 1: Preliminaries

Determine if is periodic, and if so, find the smallest (fundamental) period.

Use the graph of shown below to graph .

Identify functions and such that the given function equals

Using a graphing utility, estimate the solutions to in radians. Round answers to the nearest hundredth.

Find the composition , then determine its domain. and

Identify functions f (x) and g(x) such that given function equals (f ◦ g) (x) . tan³ x

Determine if is periodic, and if so, find the smallest (fundamental) period.

Determine if is periodic, and if so, find the smallest (fundamental) period.

Using a graphing utility, estimate the solutions to in radians. Round answers to the nearest hundredth.

An observer, standing on level ground, 100 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.7 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.

Graph and on the same axes.

Identify functions , and such that the given function equals .

Use the graph of shown below to graph .

Complete the square and explain how to transform the graph of into the graph of

Complete the square and explain how to transform the graph of into the graph of

Use the range for to determine the indicated function value. , find

Use the graph of shown below to graph .

Find the compositions f ◦ g and g ◦ f, and identify their respective domains. f (x) = x² + 9, g(x) = cos x

Use the graph of shown below to graph .

Identify functions and such that the given function equals .

Quiz 1: Preliminaries

Determine if is periodic, and if so, find the smallest (fundamental) period.

Use the graph of shown below to graph .

Identify functions and such that the given function equals

Using a graphing utility, estimate the solutions to in radians. Round answers to the nearest hundredth.

Find the composition , then determine its domain. and

Identify functions f (x) and g(x) such that given function equals (f ◦ g) (x) . tan3 x

Determine if is periodic, and if so, find the smallest (fundamental) period.

Determine if is periodic, and if so, find the smallest (fundamental) period.

Using a graphing utility, estimate the solutions to in radians. Round answers to the nearest hundredth.

An observer, standing on level ground, 100 feet from the bottom of a tower, looks at the top of the tower and notices that his angle of elevation is 0.7 radians. Estimate the height, h, of the tower, rounding your answer to the nearest tenth.

Graph and on the same axes.

Identify functions , and such that the given function equals .

Use the graph of shown below to graph .

Complete the square and explain how to transform the graph of into the graph of

Complete the square and explain how to transform the graph of into the graph of

Use the range for to determine the indicated function value. , find

Use the graph of shown below to graph .

Find the compositions f ◦ g and g ◦ f, and identify their respective domains. f (x) = x2 + 9, g(x) = cos x

Use the graph of shown below to graph .

Identify functions and such that the given function equals .

Identify functions f (x) and g(x) such that given function equals (f ◦ g) (x) . tan³ x

Find the compositions f ◦ g and g ◦ f, and identify their respective domains. f (x) = x² + 9, g(x) = cos x