Representación Gráfica de una Función Matemática. Dominio y Rango.
Introduction to Graphing Functions
Overview of Function Representation
- Profe Gabriel introduces the topic of graphing functions, focusing on establishing domain and range.
- The initial step involves assigning values to the independent variable x , typically ranging from -3 to 3 for evaluation.
Tabulation Process
- A table is created to organize the assigned values for x : -3, -2, -1, 0, 1, 2, and 3.
- The process of evaluating the function involves substituting these x values into the function f(x) = x + 1 .
Evaluating Function Values
Step-by-Step Evaluation
- For x = -3 , substituting gives f(-3) = -2 .
- Continuing with evaluations:
- For x = -2, f(-2) = -1
- For x = -1, f(-1) = 0
- For x = 0, f(0) = 1
- For x = 1, f(1) = 2
- For x = 2, f(2) = 3
- For x = 3, f(3)=4
Graphing the Function
Plotting Points on Cartesian Plane
- The horizontal axis represents values of x , while the vertical axis represents values of the function.
- Points are plotted based on evaluated coordinates:
- Point for (-3, -2)
- Point for (-1, 0)
- Point for (0, 1)
- Point for (1, 2)
- Point for (3,4)
Connecting Points
- The points form a straight line when connected; this indicates a linear function.
Understanding Domain and Range
Definitions and Concepts
- Domain refers to all possible input values (x) where the function exists; in this case from negative infinity to positive infinity.
- Range refers to all possible output values (f(x)); similarly extends from negative infinity to positive infinity.
Visualizing Domain and Range
- (557)s As we extend our evaluation beyond assigned limits:
- The domain remains continuous as it stretches infinitely in both directions.
- The range also continues infinitely upwards and downwards.
Summary of Findings
- (628)s Both domain and range are represented as intervals from negative infinity to positive infinity. This reflects that linear functions do not have restrictions within their defined parameters.