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.
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
7 answers
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.
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.
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.
Division of polynomials may result in a rational function, which is not strictly considered a polynomial function.
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)
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)
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).
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).
what is it
The correct statement is:
(c-2,y)
This point will also be on the graph of f(x).
(c-2,y)
This point will also be on the graph of f(x).
1 answer