≡Mathematics EN 9th grade: translate this: 1. Definição de função
1. Definition of a function
A function is a relation that associates each value of x with a unique value of y.
\( y = f(x) \)
👉 For each x, there is only one y.
✔ Example:
\( f(x) = 2x + 1 \)
If 𝑥 = 2, then
\( f(2) = 2 \cdot 2 + 1 = 5 \)
2. Domain of a function
It is the set of values of 𝑥 that can be used
\( D_f \)
✔ Example:
\( f(x) = \frac{1}{x} \Rightarrow x \neq 0 \)
👉 Domain: all real numbers except zero
3. Codomain (range set)
It is the set of all possible output values
\( \mathbb{R} \)
👉 Usually these are the real numbers
4. Image (values that the function assumes)
These are the values that actually appear as a result
✔ Example:
\( f(x) = x^2 \)
👉 The image consists only of positive values or zero
5. Independent and dependent variables
- Independent variable → chosen value
\( x \)
- Dependent variable → depends on x
\( y = f(x) \)
✔ Example:
\( y = 3x \)
👉 If x changes, y changes
6. Graphical Representation
It is the graph of the function on the Cartesian plane. Each point has the form:
\( (x, f(x)) \)
✔ Example:
\( f(x) = x + 1 \)
Points on the graph:
\( (0,1), (1,2), (2,3) \)
👉 Forms a straight line
QUICK TIPS FOR THE EXAM
✔ Function → each x has a unique y
✔ Domain → possible values of x
✔ Range → obtained values
✔ Graph → points (x, f(x))
✔ x independent, y dependent
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