Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).

a. 𝔂 = ƒ(x - 5)

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Start with the graph of the function 𝔂 = ƒ(x). This is your base graph.

Identify the transformation applied to the function. In this case, the transformation is 𝔂 = ƒ(x - 5).

Recognize that the expression (x - 5) inside the function indicates a horizontal shift. Specifically, it is a shift to the right.

To apply this transformation, take each point (x, y) on the original graph of 𝔂 = ƒ(x) and move it 5 units to the right. This means you will replace each x-coordinate with (x + 5).

Plot the new points to obtain the graph of 𝔂 = ƒ(x - 5). The shape of the graph remains unchanged, but its position is shifted 5 units to the right.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Function Transformation

Function transformation refers to the process of altering the graph of a function through shifts, stretches, or reflections. These transformations can change the position and shape of the graph without altering its fundamental properties. Understanding how to manipulate the function's equation allows one to predict how the graph will change.

Horizontal Shifts

A horizontal shift occurs when the graph of a function is moved left or right along the x-axis. For the function 𝔶 = ƒ(x - 5), the graph is shifted 5 units to the right. This transformation is achieved by replacing x with (x - c), where c is the number of units shifted, affecting the input values of the function.

Graphing Functions

Graphing functions involves plotting points that represent the output of a function for various input values. Understanding how to graph functions is essential for visualizing transformations. By knowing the original graph of 𝔶 = ƒ(x), one can easily apply transformations to see how the graph changes, enhancing comprehension of function behavior.

Describe how each graph is obtained from the graph of 𝔂 = ƒ(x).a. 𝔂 = ƒ(x - 5)