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
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.
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.
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.
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)
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).
what is it
The correct statement is:
(c-2,y)
This point will also be on the graph of f(x).