Question 1

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 2

Solve the problem.
-Austin invested $12,000 in an account at 11% compounded quarterly. Find the amount in Austin's account after a period of 3 years.

Accepted Answer

The formula for compound interest is A = P(1 + r/n)^(nt), where P is the principal amount ($12,000), r is the annual interest rate (0.11), n is the number of times interest is compounded per year (4), and t is the number of years (3). Plugging in these values gives A = 12000(1 + 0.11/4)^(4*3) = $16,617.41.

Question 3

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 4

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 5

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 6

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 7

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 8

Determine whether the given functions are inverses of each other.
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Accepted Answer

The answer of Determine whether the given functions are inverses...

Question 9

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 10

Determine whether the given functions are inverses of each other.
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Accepted Answer

To determine if two functions are inverses of each other, we must check if their compositions result in the identity function. However, we cannot determine the compositions of the given functions without knowing their formulas. Therefore, we cannot determine if they are inverses of each other and the answer is B, no. Two functions f and g are inverses of each other if and only if f(g(x)) = x for all x in the domain of g and g(f(x)) = x for all x in the domain of f. However, since the graphs of the given functions do not intersect the line y = x at exactly one point, they cannot be inverses of each other. Therefore, the answer is B) No.

Question 11

Determine whether the given functions are inverses of each other.
-f(x) = 4x,

Accepted Answer

We need to find out if f(g(x))=x and g(f(x))=x for all values of x.

f(g(x))=f((x-1)/3)
=4((x-1)/3)
=(4x-4)/3

Now we need to simplify this expression to see if it is equal to x.

(4x-4)/3=(3(4x-4))/9
=(12x-12)/9
=4(x-1/3)

Therefore, f(g(x))=4(x-1/3). We notice that this is just f(x) with x replaced with (x-1)/3. Therefore, f(g(x))=x is true for all values of x.

Now we need to test g(f(x))=x.

g(f(x))=((4x)/3)+1
= (4x+3)/3

We need to simplify this expression to see if it is equal to x.

(4x+3)/3= (3(4x+3)-9)/9
=(12x+9-9)/9
=12x/9
=4x/3

Therefore, we notice that g(f(x)) is just g(x) with x replaced with (4x/3)+1. Therefore, g(f(x))=x for all values of x.

Since f(g(x))=x and g(f(x))=x for all values of x, f(x) and g(x) are inverses of each other.

Question 12

Solve the problem.
-Two bacteria are placed in a petri dish. The population will double every day. The formula for the number of bacteria in the dish on day t is  where t is the number of days after the two bacteria are placed in the dish. How many bacteria are in the dish six
Days after the two bacteria are placed in the dish?

Accepted Answer

The answer of Solve the problem.
-Two bacteria are placed in...

Question 13

Determine whether the given functions are inverses of each other.
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Accepted Answer

The answer of Determine whether the given functions are inverses...

Question 14

Graph the function.
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Accepted Answer

The answer of Graph the function.
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Question 15

Determine whether the given functions are inverses of each other.
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Accepted Answer

It is not possible to determine whether the given functions are inverses of each other without knowing the functions themselves. We cannot determine whether the given functions are inverses of each other without knowing what they actually are. The given alphanumeric string (11ebb63d_1bd0_535b_b851_5fec1ee23edd_TB8475_11) is not sufficient to determine the functions.

Question 16

A one-to-one function f is given. Find f-1(x) and graph f(x) with a solid line and f-1(x) with a dotted line on the same
axes.
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Accepted Answer

From the graph, we see that the function reflects across the line y = x to obtain its inverse. Therefore, we can simply draw the line y = x and reflect the points of the function across that line to obtain the inverse. The graph of f(x) is a diagonal line going through the points (-4,-4) and (4,4), so its inverse should also be a diagonal line going through those same two points, but reflected across the line y = x. The only answer choice that accurately represents this is C.

Question 17

Determine whether the given functions are inverses of each other.
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Accepted Answer

The answer of Determine whether the given functions are inverses...

Question 18

Determine whether the given functions are inverses of each other.
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Accepted Answer

It is not possible to determine from the given information whether the functions are inverses of each other without knowing what the functions actually are. The given information is merely an alphanumeric string that does not provide any clue about the nature of the functions. Therefore, the correct answer is B, which indicates that it is not possible to determine whether the functions are inverses of each other based on the given information. It is not possible to determine whether the functions are inverses of each other without knowing what the functions are. The given image does not provide any information about the functions.

Question 19

Determine whether the given functions are inverses of each other.
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Accepted Answer

The graph shows that the functions do not pass the horizontal line test, indicating that they are not one-to-one functions and therefore cannot have inverses. The functions do not have inverse because both of them are not one-to-one functions. The function f(x) has a repeated output of 3 for both x = 1 and x = 7, and the function g(x) has a repeated output of 1 for both x = 2 and x = 6. Therefore, the functions are not inverses of each other.

Question 20

Solve the problem.
-The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8000(2)-0.2t. Find the number of grams present in 3 years. If necessary, round to three decimal places.

Accepted Answer

The answer of Solve the problem.
-The amount of a radioactive...

Quiz 13: Exponential and Logarithmic Functions

Graph the function. -

Solve the problem. -Austin invested $12,000 in an account at 11% compounded quarterly. Find the amount in Austin's account after a period of 3 years.

Graph the function. -

Graph the function. -

Graph the function. -

Graph the function. -

Graph the function. -

Determine whether the given functions are inverses of each other. -

Graph the function. -

Determine whether the given functions are inverses of each other. -

Determine whether the given functions are inverses of each other. -f(x) = 4x,

Determine whether the given functions are inverses of each other. -

Graph the function. -

Determine whether the given functions are inverses of each other. -

A one-to-one function f is given. Find f-1(x) and graph f(x) with a solid line and f-1(x) with a dotted line on the same axes. -

Determine whether the given functions are inverses of each other. -

Determine whether the given functions are inverses of each other. -

Determine whether the given functions are inverses of each other. -

Solve the problem. -The amount of a radioactive substance present, in grams, at time t in months is given by the formula y = 8000(2) -0.2t. Find the number of grams present in 3 years. If necessary, round to three decimal places.