Question
The graphs below shows g(x) , which is a translation of a parent function f(x) . Write the function rule for g(x) .
Answers
Answered by
GPT-4o mini
To provide you with the function rule for \( g(x) \), I need to know what the graphs look like or the transformations applied to the parent function \( f(x) \).
Common transformations include:
1. **Vertical shifts**: Moving the graph up or down.
- If \( g(x) = f(x) + k \), the graph of \( g(x) \) is shifted up by \( k \) units if \( k > 0 \) and down by \( k \) units if \( k < 0 \).
2. **Horizontal shifts**: Moving the graph left or right.
- If \( g(x) = f(x - h) \), the graph of \( g(x) \) is shifted right by \( h \) units if \( h > 0 \) and left by \( h \) units if \( h < 0 \).
3. **Vertical stretches and compressions**: Changing the height of the graph.
- If \( g(x) = a \cdot f(x) \), the graph is stretched vertically by a factor of \( a \) if \( a > 1 \) or compressed if \( 0 < a < 1 \).
4. **Horizontal stretches and compressions**: Affecting the width of the graph.
- If \( g(x) = f(b \cdot x) \), the graph is compressed horizontally by a factor of \( 1/b \) if \( b > 1 \) and stretched if \( 0 < b < 1 \).
5. **Reflections**: Flipping the graph over the x-axis or y-axis.
- If \( g(x) = -f(x) \), the graph is reflected over the x-axis. If \( g(x) = f(-x) \), it’s reflected over the y-axis.
If you can describe the transformations applied to \( f(x) \) to arrive at \( g(x) \) or provide details about the graph, I can help you derive the function rule for \( g(x) \).
Common transformations include:
1. **Vertical shifts**: Moving the graph up or down.
- If \( g(x) = f(x) + k \), the graph of \( g(x) \) is shifted up by \( k \) units if \( k > 0 \) and down by \( k \) units if \( k < 0 \).
2. **Horizontal shifts**: Moving the graph left or right.
- If \( g(x) = f(x - h) \), the graph of \( g(x) \) is shifted right by \( h \) units if \( h > 0 \) and left by \( h \) units if \( h < 0 \).
3. **Vertical stretches and compressions**: Changing the height of the graph.
- If \( g(x) = a \cdot f(x) \), the graph is stretched vertically by a factor of \( a \) if \( a > 1 \) or compressed if \( 0 < a < 1 \).
4. **Horizontal stretches and compressions**: Affecting the width of the graph.
- If \( g(x) = f(b \cdot x) \), the graph is compressed horizontally by a factor of \( 1/b \) if \( b > 1 \) and stretched if \( 0 < b < 1 \).
5. **Reflections**: Flipping the graph over the x-axis or y-axis.
- If \( g(x) = -f(x) \), the graph is reflected over the x-axis. If \( g(x) = f(-x) \), it’s reflected over the y-axis.
If you can describe the transformations applied to \( f(x) \) to arrive at \( g(x) \) or provide details about the graph, I can help you derive the function rule for \( g(x) \).