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# Introduction to Relations and Functions

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@PreciseLute

### What is the key distinction between relations and functions?

Relations can have multiple inputs for a single output, while functions have a one-to-one correspondence between inputs and outputs.

### Which type of relation is both reflexive and symmetric?

Equivalence relation

### What is the relationship between one-to-one (injective) functions and bijective functions?

One-to-one functions are a subset of bijective functions.

### Which type of function has the property that every element in the codomain is the image of at least one element in the domain?

<p>Onto (surjective) function</p> Signup and view all the answers

### What is the notation for a composite function?

<p>(f ∘ g)(x) = f(g(x))</p> Signup and view all the answers

### What is the purpose of function composition?

<p>To apply one function to the result of another function.</p> Signup and view all the answers

### What is a binary operation?

<p>A function that operates on pairs of elements from the same set, producing another element of the same set.</p> Signup and view all the answers

### How can functions be represented pictorially?

<p>Using Cartesian coordinates and mapping diagrams.</p> Signup and view all the answers

### Which condition is necessary for a function to be invertible?

<p>The function must be both one-to-one and onto.</p> Signup and view all the answers

### What is a real-world application of composite functions?

<p>Determining the cost of production in economics.</p> Signup and view all the answers

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