Every function is a rule which tells you how to associate inputs and outputs. The input, also known as independent variable, is often indicated with the letter 
, while the output, also known as dependent variable, is often indicated with the letter 
.
With this notation, we write 
, read "y is a function of x", in the sense that the value of the variable y depends on the value of the variable x, and f is the function that tells you how y depends on x.
In your example, you have 
, which means "subtract four times the input (4x) from 2"
So, it doesn't matter which input you chose (i.e. the value for x), because you will always have to behave this way:
- Pick an input value, x
- Multiply it by four to get 4x
- Subtract this number from 2: 2-4x
Here are some examples of explicit calculations: if I choose 
and input, the workflow will be
- Pick an input value, 2
- Multiply it by four to get 8
- Subtract this number from 2: 2-8=-6
So, if the input is 2, the output is -6
Similarly, if we choose 
as input, we have:
- Pick an input value, 0
- Multiply it by four to get 0
- Subtract this number from 2: 2-0=2
So, if the input is 0, the output is 2. And so on: for every possible value for x you have the correspondant value for y, with the function f telling you how to associate one with the other.
Measurement is the numerical quantitation of the attributes of an object or event, which can be used to compare with other objects or events. The scope and application of measurement are dependent on the context and discipline
For the zero product property questions it's choices 2 and 3 since they're quadratics factored and set equal to zero.
for the quadratic formula questions it would be answer choices 2 and 3 also because they're unfactored trinomial quadratic expressions
Alright, as we can see the large rectangle's area is 4x² + 9x + 2.
You can also see that gray rectangle's area inside the larger rectangle is
x² + 4x + 3.
So if we want to find the white area in-between the two rectangles we will need to SUBTRACT the two formulas! (Subtract the large rectangle from the smaller one)
To do so we will need to subtract the like terms.
The like terms are 4x² and x², 9x and 4x, 2 and 3!
So first we do 4x² - x² and you get 3x²
Next, we do 9x - 4x and you get 5x
Lastly, we do 2 - 3 and you get -1
Now we put our solutions together and you get...
3x² + 5x - 1
This is the are for the white region of your problem. :D glad to help
