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Mathematics for Data Science

bookIntroduction to Functions

Functions are a critical driver of math and data science. They not only define relationships between inputs and outputs, but they also analyze trends and model behavior. From machine learning models to data transformations, functions play a crucial role in decision-making.

Imagine a vending machine: you insert an input (x), and it follows a specific rule to produce a unique output (f(x)). Just like different coins provide different drinks, each input in a function maps to a single, predictable result.

Types of Functions

  • One-to-one (injective) functions: each input has a unique output. No two inputs share the same result;
f(x)=2x+3f(x) = 2x + 3
  • Many-to-one functions: multiple inputs can map to the same output;
f(x)=x2f(x) = x^2
  • Onto (surjective) functions: every possible output has at least one input mapped to it;
f(x)=x−4f(x) = x - 4
  • Into functions: some outputs remain unused, meaning the function doesn’t cover the entire codomain;
f(x)=x2f(x) = x^2
  • Bijective functions: a function that is both One-to-One and Onto, meaning it is reversible.
f(x)=3x+2f(x) = 3x + 2

1. Which function type allows multiple inputs to map to the same output?

2. Which of the following is an onto function?

question mark

Which function type allows multiple inputs to map to the same output?

Select the correct answer

question mark

Which of the following is an onto function?

Select the correct answer

Tudo estava claro?

Como podemos melhorá-lo?

Obrigado pelo seu feedback!

Seção 1. Capítulo 1

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bookIntroduction to Functions

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Functions are a critical driver of math and data science. They not only define relationships between inputs and outputs, but they also analyze trends and model behavior. From machine learning models to data transformations, functions play a crucial role in decision-making.

Imagine a vending machine: you insert an input (x), and it follows a specific rule to produce a unique output (f(x)). Just like different coins provide different drinks, each input in a function maps to a single, predictable result.

Types of Functions

  • One-to-one (injective) functions: each input has a unique output. No two inputs share the same result;
f(x)=2x+3f(x) = 2x + 3
  • Many-to-one functions: multiple inputs can map to the same output;
f(x)=x2f(x) = x^2
  • Onto (surjective) functions: every possible output has at least one input mapped to it;
f(x)=x−4f(x) = x - 4
  • Into functions: some outputs remain unused, meaning the function doesn’t cover the entire codomain;
f(x)=x2f(x) = x^2
  • Bijective functions: a function that is both One-to-One and Onto, meaning it is reversible.
f(x)=3x+2f(x) = 3x + 2

1. Which function type allows multiple inputs to map to the same output?

2. Which of the following is an onto function?

question mark

Which function type allows multiple inputs to map to the same output?

Select the correct answer

question mark

Which of the following is an onto function?

Select the correct answer

Tudo estava claro?

Como podemos melhorá-lo?

Obrigado pelo seu feedback!

Seção 1. Capítulo 1
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