Question

A naval engineer uses the function, P, to analyze the effects of water pressure on submarines. The function P(d) measures the pressure exerted by water, where d represents the depth of water in meters. Which of the following would be a possible domain?

A. d is the set of all integers

B. d is the set of all integers where d>0

C. d is the set of all rational number

D. d is the set of all rational numbers where {0 less than or equal to d less than or equal to depth of sea floor

Answer 1

[AI-generated answer — Bot GPT 3.5]

D. d is the set of all rational numbers where {0 less than or equal to d less than or equal to depth of sea floor

The domain of the function P(d) should include all possible values of depth d within the constraints of the situation, which would be rational numbers greater than or equal to zero and less than or equal to the depth of the sea floor.

Answer 2

Which of the following statements about closure is false?

A. Polynomials are closed under addition. When you add polynomials, the result will always be a polynomial.

B. Polynomials are closed under subtraction. When you subtract polynomials, the result will always be a polynomial.

C. Polynomials are closed under division. When you divide polynomials, the result will always be a polynomial.

D. Polynomials are closed under multiplication. When you multiply polynomials, the result will always be a polynomial.

Answer 3

[AI-generated answer — Bot GPT 3.5]

C. Polynomials are closed under division. When you divide polynomials, the result will not always be a polynomial.

Division of polynomials may result in a rational function, which is not strictly considered a polynomial function.

Answer 4

Consider the function f(x) = x(x-4).

If the point (2 + c,y) is on the graph of f(x), the following point will also be on the graph of f(x):

select a value

(c-2,y)
(2-c,y)

Answer 5

[AI-generated answer — Bot GPT 3.5]

Let's first find the value of y when x = 2 + c:

f(2 + c) = (2 + c)((2 + c) - 4)
f(2 + c) = (2 + c)(2 + c - 4)
f(2 + c) = (2 + c)(c - 2)
f(2 + c) = 2c + c^2 - 4 - 2c
f(2 + c) = c^2 - 4

Therefore, the coordinates for the point (2 + c, y) will be (2 + c, c^2 - 4).

Now, let's consider the point (c-2, y):

f(c - 2) = (c - 2)((c - 2) - 4)
f(c - 2) = (c - 2)(c - 2 - 4)
f(c - 2) = (c - 2)(c - 6)
f(c - 2) = c^2 - 8c + 12

Therefore, the coordinates for the point (c - 2, y) will be (c - 2, c^2 - 8c + 12).

Since the function f(x) = x(x-4) is symmetric around x = 2, we can see that the functions at points (2 + c, y) and (c - 2, y) are not equal. Therefore, the second statement " (c-2,y) " will not be on the graph of f(x).

Answer 6

what is it

Answer 7

[AI-generated answer — Bot GPT 3.5]

The correct statement is:

(c-2,y)

This point will also be on the graph of f(x).