Math for - Functions

A machine performs an operation on an input number. The operation is defined as: "multiply by 3, then add 5". Let $f(x)$ represent this operation where $x$ is the input number.
1. Write an expression for $f(x)$.
  Answer (a):
2. Calculate $f(4)$.
  Answer (b):
3. Calculate $f(-2)$.
  Answer (c):
An engineer determines that the cost $C$ (in dollars) to produce $n$ units of a small sensor is given by the function $C(n) = 15n + 250$.
1. What is the cost to produce 10 sensors?
  Answer (a):
2. If the budget for sensor production is $1000, how many sensors can be produced at most (assuming only whole sensors can be produced)?
  Answer (b):
Let a function $g(x)$ be defined as $g(x) = 5x - 3$. Let another function $h(x)$ be defined as $h(x) = x + 8$.
1. Calculate $g(2)$.
  Answer (a):
2. Calculate $h(1)$.
  Answer (b):
3. Calculate $g(h(1))$. (This means: first calculate $h(1)$, then use that result as the input for $g$).
  Answer (c):
The formula to convert temperature from Celsius ($C$) to Fahrenheit ($F$) is given by the function $T(C) = \frac{9}{5}C + 32$.
1. In this function, what is the input variable (parameter)?
  Answer (a):
2. What does $T(C)$ represent (the output)?
  Answer (b):
3. If the temperature in a room is $25^\circ C$, what is the temperature in Fahrenheit?
  Answer (c):
Consider a function $P(s) = 4s$, which represents the perimeter of a square with side length $s$.
1. If the side length $s = 7$ cm, what is the perimeter?
  Answer (a):
2. What if the perimeter $P(s)$ is 36 cm? What is the side length $s$?
  Answer (b):
3. If the side length is doubled, say to $s_{new} = 2s_{original}$, how does the new perimeter $P(s_{new})$ relate to the original perimeter $P(s_{original})$? Explain your reasoning.
  Answer (c):