key term - F(x - h)

Definition

The expression f(x - h) represents a horizontal shift of the function f(x). The function is shifted h units to the right if h is positive, or h units to the left if h is negative. This transformation is known as a horizontal shift and is an important concept in the study of function transformations.

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.
2. If h is positive, the function is shifted to the right by h units. If h is negative, the function is shifted to the left by |h| units.
3. Horizontal shifts do not affect the shape or orientation of the function's graph, but rather move the entire graph left or right.
4. Horizontal shifts can be combined with other transformations, such as vertical shifts, reflections, and scalings, to create more complex transformations of functions.
5. Understanding horizontal shifts is crucial for analyzing and graphing transformed functions, which is a common topic in college algebra and precalculus courses.

Review Questions

• Explain the effect of the expression f(x - h) on the graph of the parent function f(x).
  • The expression f(x - h) represents a horizontal shift of the parent function f(x). If h is positive, the graph of the function is shifted h units to the right. If h is negative, the graph is shifted |h| units to the left. This transformation moves the entire graph left or right without changing its shape or orientation.
• Describe how the value of h in the expression f(x - h) determines the direction and magnitude of the horizontal shift.
  • The value of h in the expression f(x - h) directly determines the direction and magnitude of the horizontal shift. If h is positive, the function is shifted to the right by h units. If h is negative, the function is shifted to the left by |h| units. The absolute value of h represents the distance the function is shifted along the x-axis, while the sign of h indicates the direction of the shift.
• Analyze how horizontal shifts can be combined with other function transformations to create more complex transformations.
  • Horizontal shifts can be combined with other transformations, such as vertical shifts, reflections, and scalings, to create more intricate transformations of functions. For example, the expression $f(-2x + 3)$ represents a horizontal stretch by a factor of $-2$, followed by a horizontal shift of 3 units to the right. By understanding how to apply multiple transformations in succession, students can graph and analyze a wide variety of transformed functions, which is an essential skill in college algebra and precalculus.

Related terms

Horizontal Shift:

A transformation of a function where the graph is moved left or right without changing its shape or orientation.

Function Transformation: The process of modifying the graph of a function by applying various transformations such as shifts, reflections, and scalings.

Parent Function:

The original, untransformed function that serves as the basis for applying transformations.