Compare the graphs and determine which one could be the graph of a square root function.(1 point)

Question

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.

Answer 1

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.