Question
what is a translation that shifts the graph of a function horizontally
horizontal compression or a horizontal reflection or a horizontal stretch or horizontal shift
horizontal compression or a horizontal reflection or a horizontal stretch or horizontal shift
Answers
GPT-4o mini
A translation that shifts the graph of a function horizontally is called a **horizontal shift**.
In mathematical terms, if you have a function \( f(x) \), a horizontal shift to the right by \( h \) units is represented as \( f(x - h) \), and a horizontal shift to the left by \( h \) units is represented as \( f(x + h) \).
To clarify the other terms:
- **Horizontal compression** refers to narrowing the graph (making it steeper), which is often defined mathematically by multiplying the input by a factor greater than 1 (e.g., \( f(kx) \) for \( k > 1 \)).
- **Horizontal reflection** refers to flipping the graph across the vertical axis, represented by \( f(-x) \).
- **Horizontal stretch** means widening the graph, which can be described by multiplying the input by a factor less than 1 (e.g., \( f(kx) \) for \( 0 < k < 1 \)).
So, the correct choice for shifting the graph horizontally is **horizontal shift**.
In mathematical terms, if you have a function \( f(x) \), a horizontal shift to the right by \( h \) units is represented as \( f(x - h) \), and a horizontal shift to the left by \( h \) units is represented as \( f(x + h) \).
To clarify the other terms:
- **Horizontal compression** refers to narrowing the graph (making it steeper), which is often defined mathematically by multiplying the input by a factor greater than 1 (e.g., \( f(kx) \) for \( k > 1 \)).
- **Horizontal reflection** refers to flipping the graph across the vertical axis, represented by \( f(-x) \).
- **Horizontal stretch** means widening the graph, which can be described by multiplying the input by a factor less than 1 (e.g., \( f(kx) \) for \( 0 < k < 1 \)).
So, the correct choice for shifting the graph horizontally is **horizontal shift**.