Andres buys a bag of cookies that contains 6 chocolate chip cookies, 5 peanut butter cookies, 8 sugar cookies and 9 oatmeal cook
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Answer:
1) f(x) is not a function
2) g(x) is a function.
Step-by-step explanation:
Function is defined as a relationship between the independent variable and the dependent variable
If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of y is determined, then y is said to be a function of the independent variable
The above function can be represented by y = f(x). f(x) can also been represented g(x) and P(x) functions of the independent variable x, when the function is unknown or unspecified.
Two laws to become a function:
a) Every element in X is related to some element in Y.
This relationship is commonly symbolized as y = f(x). In addition to f(x), other abbreviated symbols such as g(x) and P(x) are often used to represent functions of the independent variable x, especially when the nature of the function is unknown or unspecified.
Two rules to become a function:
a)"Each element" means that every element in X is related to some element in Y.
But some elements of Y may not assigned to x
b) A function is assigned to a single value. It will not give back 2 or more elements for the same input.
One-to-many is unaccepted, while many-to-one is accepted
If the relationship does not satisfies those two rules then it is not a function. we can say that the given relationship not a function.
1) Let f(x) be the function
Given x is domain ie, and y=f(x) ie,
is the range of x
By the definition of function, f(x) does not satisfies the rules to be a function because f(-2)=2 and f(-2)=3 So it assigns two values.
Therefore f(x) is not a function
2) Let g(x) be the function
x is domain ie, and y=g(x) ie,
is the range of x
By the definition function, g(x) satisfies the rules to be a function because g(-2)=3 , g(-1)=3.5,g(0)=2 and g(1)=2 So it assigns exactly one value.
Therefore g(x) is a function.
From the problem, the vertex = (0, 0) and the focus = (0, 3)
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm
From the attached graphic, the equation can be expressed as:
(x -h)^2 = 4p (y -k)
where (h, k) are the (x, y) values of the vertex (0, 0)
The "p" value is the difference between the "y" value of the focus and the "y" value of the vertex.
p = 3 -0
p = 3
So, we form the equation
(x -0)^2 = 4 * 3 (y -0)
x^2 = 12y
To put this in proper quadratic equation form, we divide both sides by 12
y = x^2 / 12
Source:
http://www.1728.org/quadr4.htm