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Compare the graphs and determine which one could be the graph of a square root function.(1 point) Responses A coordinate plane'...Question
Compare the graphs and determine which one could be the graph of a square root function.(1 point)
Responses
A coordinate plane's axes range from negative 3 to 3, both by 1-unit increments. An S-shaped curve is plotted passing through 3 marked points.
Image with alt text: A coordinate plane's axes range from negative 3 to 3, both by 1-unit increments. An S-shaped curve is plotted passing through 3 marked points.
A coordinate plane's x-axis ranges from negative 3 to 3 and its y-axis ranges from negative 1 to 4, both by 1-unit increments. A concave up parabola is drawn passing through 3 marked points in the first and second quadrants.
Image with alt text: A coordinate plane's x-axis ranges from negative 3 to 3 and its y-axis ranges from negative 1 to 4, both by 1-unit increments. A concave up parabola is drawn passing through 3 marked points in the first and second quadrants.
A coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A straight line is plotted passing through 3 marked points in the first and third quadrants.
Image with alt text: A coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A straight line is plotted passing through 3 marked points in the first and third quadrants.
A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 4, both by 1-unit increments. A curve is plotted in the first quadrant. It passes through 3 marked points.
Image with alt text: A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 4, both by 1-unit increments. A curve is plotted in the first quadrant. It passes through 3 marked points.
Responses
A coordinate plane's axes range from negative 3 to 3, both by 1-unit increments. An S-shaped curve is plotted passing through 3 marked points.
Image with alt text: A coordinate plane's axes range from negative 3 to 3, both by 1-unit increments. An S-shaped curve is plotted passing through 3 marked points.
A coordinate plane's x-axis ranges from negative 3 to 3 and its y-axis ranges from negative 1 to 4, both by 1-unit increments. A concave up parabola is drawn passing through 3 marked points in the first and second quadrants.
Image with alt text: A coordinate plane's x-axis ranges from negative 3 to 3 and its y-axis ranges from negative 1 to 4, both by 1-unit increments. A concave up parabola is drawn passing through 3 marked points in the first and second quadrants.
A coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A straight line is plotted passing through 3 marked points in the first and third quadrants.
Image with alt text: A coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. A straight line is plotted passing through 3 marked points in the first and third quadrants.
A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 4, both by 1-unit increments. A curve is plotted in the first quadrant. It passes through 3 marked points.
Image with alt text: A coordinate plane's x-axis ranges from negative 2 to 6 and its y-axis ranges from negative 2 to 4, both by 1-unit increments. A curve is plotted in the first quadrant. It passes through 3 marked points.
Answers
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Answered by
GPT-4o mini
To determine which graph could represent a square root function, we need to consider the characteristics of square root functions.
1. **Domain**: The domain of a square root function \( f(x) = \sqrt{x} \) is \( x \geq 0 \). This means the graph will only exist in the right half of the coordinate plane (first quadrant), and will not have any negative x-values.
2. **Shape**: The graph of a square root function is a curve that starts from the origin (0,0) and rises slowly, becoming less steep as x increases. It looks like half of a sideways parabola.
3. **Y-values**: The only y-values produced by a square root function are non-negative, as square roots cannot yield negative outputs.
Based on these characteristics, we can analyze the provided graph descriptions:
- **Graph 1** (S-shaped curve): This does not represent a square root function due to its S-shaped nature, indicating it likely represents some other function.
- **Graph 2** (concave up parabola): While this graph may resemble the shape of a square root function in one part, parabola graphs can extend in both directions and may have negative y-values, so it doesn't represent a square root function directly.
- **Graph 3** (straight line): A straight line could represent a linear function, not a square root function, so it's not the correct answer.
- **Graph 4** (curve in the first quadrant): This graph fits the characteristics of a square root function. It is in the first quadrant, indicating non-negative x and y values, and likely has the correct shape (curving upwards but flattening out as x increases).
Given this analysis, **Graph 4** is the one that could represent the graph of a square root function.
1. **Domain**: The domain of a square root function \( f(x) = \sqrt{x} \) is \( x \geq 0 \). This means the graph will only exist in the right half of the coordinate plane (first quadrant), and will not have any negative x-values.
2. **Shape**: The graph of a square root function is a curve that starts from the origin (0,0) and rises slowly, becoming less steep as x increases. It looks like half of a sideways parabola.
3. **Y-values**: The only y-values produced by a square root function are non-negative, as square roots cannot yield negative outputs.
Based on these characteristics, we can analyze the provided graph descriptions:
- **Graph 1** (S-shaped curve): This does not represent a square root function due to its S-shaped nature, indicating it likely represents some other function.
- **Graph 2** (concave up parabola): While this graph may resemble the shape of a square root function in one part, parabola graphs can extend in both directions and may have negative y-values, so it doesn't represent a square root function directly.
- **Graph 3** (straight line): A straight line could represent a linear function, not a square root function, so it's not the correct answer.
- **Graph 4** (curve in the first quadrant): This graph fits the characteristics of a square root function. It is in the first quadrant, indicating non-negative x and y values, and likely has the correct shape (curving upwards but flattening out as x increases).
Given this analysis, **Graph 4** is the one that could represent the graph of a square root function.
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