F(x + h)

Definition

The expression f(x + h) represents a transformation of the original function f(x) by shifting the input variable x by a constant value h. This transformation is known as a horizontal shift, as it moves the function left or right on the coordinate plane without changing its shape or orientation.

5 Must Know Facts For Your Next Test

1. The value of h in the expression f(x + h) determines the direction and magnitude of the horizontal shift. A positive value of h shifts the function to the left, while a negative value shifts it to the right.
2. Horizontal shifts preserve the shape and orientation of the original function, but change its position on the coordinate plane.
3. Horizontal shifts can be used to model real-world phenomena, such as the movement of objects or the changes in a function's domain.
4. The expression f(x + h) is often used in the context of function transformations, where it is combined with other transformations like vertical shifts, reflections, and dilations.
5. Understanding the behavior of f(x + h) is crucial for analyzing and graphing transformed functions, as well as for solving problems involving function composition.

Review Questions

• Explain how the value of h in the expression f(x + h) affects the horizontal shift of the function.
  • The value of h in the expression f(x + h) determines the direction and magnitude of the horizontal shift of the function. A positive value of h will shift the function to the left, while a negative value of h will shift the function to the right. The larger the absolute value of h, the greater the distance the function is shifted along the x-axis. This horizontal shift preserves the shape and orientation of the original function, but changes its position on the coordinate plane.
• Describe how the expression f(x + h) is used in the context of function transformations.
  • The expression f(x + h) is often used in the context of function transformations, where it is combined with other transformations like vertical shifts, reflections, and dilations. By understanding the behavior of f(x + h), you can analyze and graph transformed functions, as well as solve problems involving function composition. The horizontal shift represented by f(x + h) is a key component of these more complex function transformations, allowing you to modify the domain and position of a function without changing its essential characteristics.
• Analyze how the expression f(x + h) can be used to model real-world phenomena.
  • The expression f(x + h) can be used to model real-world phenomena that involve the movement or change of a function over time or space. For example, the motion of an object along a path can be represented by a function f(x), where x represents the position and f(x) represents the object's location. The expression f(x + h) can then be used to describe how the object's position changes as time (or another variable) progresses, with h representing the change in the independent variable. This allows you to analyze and predict the behavior of the object's movement, which is useful in fields like physics, engineering, and even finance and economics.

Related terms

Horizontal Shift:

A transformation that moves a function left or right on the coordinate plane without changing its shape or orientation.

Function Transformation: The process of modifying the graph of a function by applying operations such as translations, reflections, stretches, or compressions.

Function Composition:

The combination of two or more functions, where the output of one function becomes the input of the next function.