Some people think of functions as “mathematical machines.” Imagine you have a machine that changes a number according to a specific rule, such as “multiply by 3 and add 2” or “divide by 5, add 25, and multiply by −1.” If you put a number into the machine, a new number will pop out the other end, having been changed according to the rule. The number that goes in is called the input, and the number that is produced is called the output.
You can also call the machine “f” for function. If you put x into the box, f(x),comes out. Mathematically speaking, x is the input, or the “independent variable,” and f(x) is the output, or the “dependent variable,” since it depends on the value of x.
f(x)= 4x + 1 is written in function notation and is read “f of x equals 4x plus 1.” It represents the following situation: A function named f acts upon an input, x, and produces f(x) which is equal to 4x + 1. This is the same as the equation as y = 4x + 1.
Function notation gives you more flexibility because you don’t have to use y for every equation. Instead, you could use f(x) or g(x) or c(x). This can be a helpful way to distinguish equations of functions when you are dealing with more than one at a time.
You could write the formula for perimeter, P = 4s, as the function p(x) = 4x, and the formula for area, A = x2, as a(x) = x2. This would make it easy to graph both functions on the same graph without confusion about the variables.
Answer:
The angle of elevation of the sun is 
.
Step-by-step explanation:
Let 
be the angle of elevation of the sun as shown in the diagram.
Then the side length which is 
feet is opposite to and the side length which is 
feet is adjacent to .
Therefore we use the trigonometric ratio that involves the opposite and adjacent sides, which is the tangent ratio.
We solve for to get,
To the nearest degree, the angle of elevation is
Answer:
The shape remains a square, but the size of the cross sction increases.
Answer:
f(-3) = -4
Step-by-step explanation:
f(-3) = -(-3) - 7
= 3 - 7
= -4
Answer:
w = -6
Step-by-step explanation:
w-10= .5w -7
w = .5w +3
-0.5w = 3
w = -6
