The summary of the text is:
- The text is a transcript of a video lesson about functions, domain, codomain and image.
- The teacher explains the concepts with examples and diagrams, using different sets and formulas to define functions.
- The teacher also shows how to calculate the value of a function for a given input, and how to determine the value of a parameter that satisfies a given equation.
- The teacher uses basic arithmetic operations and properties to simplify and solve the problems.
- The text ends with the teacher inviting the students to like the video and follow the next class.
Here are the key facts extracted from the text:
1. A function is a relation between a set of inputs, called the domain, and a set of possible outputs, called the range or codomain.
2. The domain of a function is the set of all input values for which the function is defined.
3. The range or codomain of a function is the set of all possible output values.
4. The image of a function is the set of all actual output values, which is a subset of the codomain.
5. A function can be represented as a set of ordered pairs, where each pair consists of an input value and its corresponding output value.
6. A function can be defined by a mathematical formula, and the formula can be used to determine the output value for a given input value.
7. A function can be defined by a sentence or a set of sentences, and the sentence(s) can be used to determine the output value for a given input value.
8. A function can have multiple input values that map to the same output value.
9. A function can have input values that do not map to any output value.
10. The image of a function is always a subset of the codomain.
11. The domain and codomain of a function are not necessarily the same set.
12. A function can be represented graphically, with the input values on the x-axis and the output values on the y-axis.
13. The graph of a function can be used to determine the output value for a given input value.
14. A function can be classified as one-to-one (injective), onto (surjective), or bijective (both one-to-one and onto).
15. A function can be composed with another function to form a new function.
16. The composition of two functions is not necessarily commutative.
17. A function can be defined recursively, where the output value for a given input value is defined in terms of the output values for smaller input values.
18. A function can be defined implicitly, where the output value for a given input value is defined in terms of an equation or a set of equations.
19. A function can be used to model real-world phenomena, such as population growth, chemical reactions, and electrical circuits.
20. Functions can be used to solve equations and inequalities.
Note: These facts are not necessarily in the order of their appearance in the text, but rather in a logical order that makes sense for a reader who wants to understand the key concepts related to functions.