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## Functions

Functions map an input to an output. For example, the function f(x) = 2x takes an input, x, and multiplies it by two. An input of x = 2 gives you an output of 4. Learn all about functions.

# Function Terminology

If we have a real-valued function $$f(x) = x^2 + 27$$, the values of $$f(x)$$ will necessarily fall in the following range:

$a \leq f(x).$

What is the value of $$a$$?

Consider two sets: $$X = \{ a, b, c, d \}, \ Y = \{ 1, 2, 3 \}.$$

If a function is defined from $$X$$ to $$Y$$, what is the maximum possible number of such functions?

For two sets $X=\{a,b,c\}, Y=\{7, 11, 13, 17, 20, 32\},$ $$f$$ is an injective function from $$X$$ to $$Y$$. If $$f(a)=7$$ and $$f(b)=17$$, what is the sum of all the elements of $$Y$$ that can possibly be the value of $$f(c)$$?

Given that the domain and codomain of the function $$y=\sqrt{169-x^2}$$ are restricted to the real numbers, how many elements of the domain of $$y=\sqrt{169-x^2}$$ are integers?

For two sets $X=\{-1,1,a\}, Y=\{3,4, b\},$ $$f(x)=x^3+4$$ is a bijective function from $$X$$ to $$Y$$. What is the value of $$a+b$$?

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