F(x/b)

Definition

The term f(x/b) represents a transformation of a function f(x) where the input variable x is divided by a constant b. This transformation is known as a horizontal scaling or stretching of the original function.

5 Must Know Facts For Your Next Test

1. The value of b determines the degree of horizontal scaling or stretching of the function f(x).
2. If $b > 1$, the function f(x/b) is horizontally stretched by a factor of b.
3. If $0 < b < 1$, the function f(x/b) is horizontally compressed by a factor of b.
4. Horizontal scaling does not affect the vertical scale or range of the function.
5. Horizontal scaling can be used to transform the domain of a function, allowing for the exploration of different input values.

Review Questions

• Explain how the value of b affects the transformation of f(x) to f(x/b).
  • The value of b in the transformation f(x/b) determines the degree of horizontal scaling or stretching of the original function f(x). If $b > 1$, the function is horizontally stretched by a factor of b, making it appear more spread out. If $0 < b < 1$, the function is horizontally compressed by a factor of b, making it appear more condensed. The vertical scale or range of the function remains unchanged, but the domain is transformed, allowing for the exploration of different input values.
• Describe the relationship between horizontal scaling and the domain of a function.
  • Horizontal scaling, as represented by the transformation f(x/b), can be used to transform the domain of a function. By dividing the input variable x by the constant b, the domain of the original function f(x) is effectively scaled or stretched. This allows for the exploration of different input values that may not have been accessible in the original function. The relationship between horizontal scaling and the domain of a function is crucial in understanding how transformations can be used to analyze and manipulate the behavior of functions.
• Analyze the effects of horizontal scaling on the graph of a function and explain how it differs from vertical scaling.
  • Horizontal scaling, as represented by the transformation f(x/b), affects the width or horizontal scale of a function's graph, without changing the vertical scale or range. This is in contrast to vertical scaling, where the function is transformed by multiplying the output variable f(x) by a constant. Horizontal scaling stretches or compresses the function horizontally, making it appear more spread out or condensed, respectively, while vertical scaling stretches or compresses the function vertically, affecting the range of output values. Understanding the distinct effects of horizontal and vertical scaling is crucial in analyzing and transforming the behavior of functions.

Related terms

Horizontal Scaling: A transformation that changes the width or horizontal scale of a function, without affecting the vertical scale.

Horizontal Stretching: A transformation that increases the width or horizontal scale of a function, making it appear more spread out.

Horizontal Compression: A transformation that decreases the width or horizontal scale of a function, making it appear more condensed.