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Comparing Shapes of Functions Quick Check

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

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 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 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.

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.

1 answer

To determine which graph could represent a square root function, we need to understand the characteristics of square root functions.

A square root function is typically defined by \(y = \sqrt{x}\) and has the following characteristics:

  • It only exists for non-negative values of \(x\) (i.e., \(x \geq 0\)).
  • The graph starts from the origin (0,0) and gradually increases, curving upwards.
  • The graph is not defined for negative values of \(x\) and does not extend into the negative \(y\) values.

Now, let's analyze the options provided:

  1. First graph: A concave up parabola in the first and second quadrants. This does not represent a square root function since a parabola can extend into both negative and positive \(y\) values.

  2. Second graph: An S-shaped curve. This resembles the graph of a cubic function, not a square root function.

  3. Third graph: A curve in the first quadrant passing through three marked points. If this curve starts at the origin and only appears in the first quadrant, it could represent a square root function.

  4. Fourth graph: A straight line in both the first and third quadrants. This cannot represent a square root function, which is not linear.

Given this analysis, the third graph is the most likely candidate to represent a square root function.