#4 Grafik & Fungsi | KALKULUS

Summary

In this educational video, M Rizky Fadhilah introduces viewers to the concept of mathematical functions and their graphical representations. The video covers the definition of functions, including the distinction between domain, codomain, and range. It then explains how to graph linear and quadratic functions, using practical examples like plotting the function y = 2x - 3 and y = x² - 9. The tutorial emphasizes step-by-step methods to determine the domain, codomain, and range, before illustrating how to sketch the graphs. The video aims to provide a clear, practical understanding of function graphing.

Takeaways

• 😀 A function in mathematics is a mapping of each element of a set (domain) to an element of another set (codomain).
• 😀 The domain is the set of input values, while the codomain is the set of possible output values. The range is the actual set of outputs obtained from the function.
• 😀 An example of a domain and codomain relationship is: for domain {1, 2, 3}, the codomain could be {a, b, c, d, e}, with the corresponding relations being (1 -> b), (2 -> d), (3 -> a).
• 😀 The key difference between domain and codomain is that the domain refers to the 'source' set, while the codomain is the 'destination' set.
• 😀 The range of a function is the set of outputs derived from the relationship between the domain and codomain.
• 😀 A linear function has a graph that forms a straight line. For example, the function y = 2x - 3 represents a linear relationship.
• 😀 When creating a graph of a linear function, first determine the domain, then calculate the corresponding y-values (codomain). Finally, plot the points and draw the line.
• 😀 The steps to graph a linear function include determining the domain (e.g., x > 2 and x ≤ 6), calculating the corresponding y-values, and plotting the points on a graph.
• 😀 A quadratic function involves an equation where the highest power of x is squared (e.g., y = x^2 - 9). The graph of a quadratic function forms a parabola.
• 😀 In quadratic functions, the vertex is the point where the parabola either opens upwards or downwards. For the function y = x^2 - 9, the vertex is at (0, -9).

Q & A

What is a function in mathematical terms?

A function in mathematics is a mapping from each member of a set (called the domain) to another member of a different set (called the codomain). The relationship between these two sets is defined by the function.

What is the difference between the domain and the codomain?

The domain refers to the set of input values, while the codomain refers to the set of possible output values. The range, however, is the set of actual output values corresponding to the inputs.

What is the concept of range in a function?

The range of a function is the set of actual output values that result from applying the function to the domain. It can be thought of as the 'result' of the function's mapping.

What is the graph of a linear function like?

The graph of a linear function is a straight line. In the video, the example given was y = 2x - 3, which forms a line on a coordinate plane.

How do you graph the function y = 2x - 3 with constraints x > 2 and x ≤ 6?

First, determine the domain, which is the range of x values between 3 and 6. Then, calculate the corresponding y values by substituting the x values into the function. Plot the points (3, 3), (4, 5), (5, 7), and (6, 9) and connect them to form the graph.

What is a quadratic function and how does its graph look?

A quadratic function is a mathematical expression involving x raised to the power of 2, such as y = x^2 - 9. The graph of a quadratic function is a curve, known as a parabola, that opens upwards or downwards depending on the coefficients.

How do you graph the quadratic function y = x^2 - 9?

To graph y = x^2 - 9, first calculate the domain and the corresponding codomain by plugging in different values of x into the function. For example, for x = -3, y = 0, and for x = 3, y = 0. Then, plot the points and draw the parabola.

What is the significance of the vertex in a quadratic function's graph?

The vertex of a quadratic function is the highest or lowest point on its graph, depending on whether the parabola opens upwards or downwards. In the case of y = x^2 - 9, the vertex is at (0, -9).

What are the key differences between linear and quadratic functions in terms of their graphs?

Linear functions have straight-line graphs, while quadratic functions have curved graphs (parabolas). Linear functions can have any slope, but quadratic functions have a constant rate of change that is always changing.

What is the method to find the domain and codomain of a quadratic function?

To find the domain, identify the possible values of x that satisfy the function’s constraints. To find the codomain, calculate the corresponding y values for the x values within the domain. For y = x^2 - 9, the codomain is determined by squaring x values and subtracting 9.