Question
Which graph shows the parent function f(x)=x2 horizontally compressed to form the graph of y=f(3x) ?(1 point) Responses Image with alt text: An upward parabola passes through 3 plotted points. The x-axis ranges from negative 5 to 6 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments. Image with alt text: An upward parabola passes through 3 plotted points. The x-axis ranges from negative 5 to 5 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments. Image with alt text: An upward parabola passes through 3 plotted points. The x-axis ranges from negative 10 to 10 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments. Image with alt text: An upward parabola passes through 3 plotted points. The x-axis ranges from negative 5 to 5 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
Answers
GPT-4o mini
To find the graph representing the function \( y = f(3x) \), where \( f(x) = x^2 \), we need to understand how the function is transformed.
The transformation from \( f(x) \) to \( f(3x) \) indicates a horizontal compression by a factor of \( \frac{1}{3} \). This means the graph will be "squeezed" towards the y-axis. For example, a point \( (x, f(x)) \) on the original parabola will move to the point \( \left(\frac{x}{3}, f(x)\right) \) on the compressed function.
### Characteristics of the graphs:
- The vertex of the function remains at the origin (0,0).
- The width of the graph will be reduced compared to that of the parent function \( y = x^2 \).
### Examining the choices:
- Look for a graph of a parabola that appears narrower than the standard \( y = x^2 \) graph.
- Verify that the x-axis range is smaller in magnitude compared to the standard parent function, with notable distinctness between the ranges.
Based on typical behavior of parabolas and the transformation described, the answer should be a graph that retains the shape of a parabola but is more narrow than it normally would be.
If you provide the images or a more detailed description of each, I can help you identify the correct one!
The transformation from \( f(x) \) to \( f(3x) \) indicates a horizontal compression by a factor of \( \frac{1}{3} \). This means the graph will be "squeezed" towards the y-axis. For example, a point \( (x, f(x)) \) on the original parabola will move to the point \( \left(\frac{x}{3}, f(x)\right) \) on the compressed function.
### Characteristics of the graphs:
- The vertex of the function remains at the origin (0,0).
- The width of the graph will be reduced compared to that of the parent function \( y = x^2 \).
### Examining the choices:
- Look for a graph of a parabola that appears narrower than the standard \( y = x^2 \) graph.
- Verify that the x-axis range is smaller in magnitude compared to the standard parent function, with notable distinctness between the ranges.
Based on typical behavior of parabolas and the transformation described, the answer should be a graph that retains the shape of a parabola but is more narrow than it normally would be.
If you provide the images or a more detailed description of each, I can help you identify the correct one!