Question
Which graph shows the parent function f(x)=x2
horizontally compressed to form the graph of y=f(3x)
?(1 point)
Responses
A. 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 6 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
b. 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 10 to 10 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
C. 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 5 to 5 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
D. 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.
horizontally compressed to form the graph of y=f(3x)
?(1 point)
Responses
A. 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 6 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
b. 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 10 to 10 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
C. 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 5 to 5 in 1-unit increments and the y-axis ranges from 0 to 10 in 1-unit increments.
D. 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
There are no human answers yet.
Answered by
GPT-4o mini
To determine which graph illustrates the transformation from the parent function \( f(x) = x^2 \) to the transformed function \( y = f(3x) \), we need to understand the effect of the transformation on the graph.
The function \( y = f(3x) \) represents a horizontal compression of the parent function. Specifically, it compresses the graph of \( f(x) \) horizontally by a factor of \( \frac{1}{3} \). This means that the points on the graph will get closer to the y-axis.
For the parent function \( f(x) = x^2 \):
- The original key points are (0, 0), (1, 1), and (-1, 1).
- After applying the transformation, the new key points will be (0, 0), \( \left(\frac{1}{3}, 1\right) \), and \( \left(-\frac{1}{3}, 1\right) \).
Considering this, the potential candidates for the graph showing \( y = f(3x) \) should display a narrower parabola. Given the choices:
- **Graph A**: x-axis ranges from -5 to 6, indicating a significant range but may not show enough detail at the peak around the transformed key points.
- **Graph B**: x-axis ranges from -10 to 10, which is very broad and may not show the effect of compression strongly.
- **Graph C**: x-axis ranges from -5 to 5, which might allow us to see the points more clearly.
- **Graph D**: This is identical to Graph C, just noting that both have the same range.
Since both Graph C and D have the same x-axis restrictions and show a horizontally compressed parabola, any could fit the description, but as per the response designations, they represent similar graphed behaviours, displaying a narrower parabola.
Without more specific points or images, **both Graph C and D would effectively show \( y = f(3x) \)**, assuming they visually represent the characteristics of a compressed parabola. However, typically only one option will be designated as the answer.
If forced to choose from the provided options, I would suggest **C or D**; both are acceptable. If only one option must be chosen based on your context, please select one based on other depicted characteristics or available output not described here.
The function \( y = f(3x) \) represents a horizontal compression of the parent function. Specifically, it compresses the graph of \( f(x) \) horizontally by a factor of \( \frac{1}{3} \). This means that the points on the graph will get closer to the y-axis.
For the parent function \( f(x) = x^2 \):
- The original key points are (0, 0), (1, 1), and (-1, 1).
- After applying the transformation, the new key points will be (0, 0), \( \left(\frac{1}{3}, 1\right) \), and \( \left(-\frac{1}{3}, 1\right) \).
Considering this, the potential candidates for the graph showing \( y = f(3x) \) should display a narrower parabola. Given the choices:
- **Graph A**: x-axis ranges from -5 to 6, indicating a significant range but may not show enough detail at the peak around the transformed key points.
- **Graph B**: x-axis ranges from -10 to 10, which is very broad and may not show the effect of compression strongly.
- **Graph C**: x-axis ranges from -5 to 5, which might allow us to see the points more clearly.
- **Graph D**: This is identical to Graph C, just noting that both have the same range.
Since both Graph C and D have the same x-axis restrictions and show a horizontally compressed parabola, any could fit the description, but as per the response designations, they represent similar graphed behaviours, displaying a narrower parabola.
Without more specific points or images, **both Graph C and D would effectively show \( y = f(3x) \)**, assuming they visually represent the characteristics of a compressed parabola. However, typically only one option will be designated as the answer.
If forced to choose from the provided options, I would suggest **C or D**; both are acceptable. If only one option must be chosen based on your context, please select one based on other depicted characteristics or available output not described here.
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