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Use the image to answer the question.

A coordinate plane's axes range from negative 2 to 4, both by 1-unit increments. A solid curve is plotted passing through the first quadrant.

Select the option that matches the graph.

Option #1: The graph of the function matches f(x)=2^3√x−−

Option #2: The graph of the function matches f(x)=2√x−− .

(1 point)
Option #_
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1 answer

I cannot view images directly. However, I can help you analyze the function's characteristics based on the provided options.

Let’s examine the two functions:

  1. Option #1: f(x) = 2√x

    • This function is a simple square root function multiplied by 2. It starts at (0, 0) and increases as x increases.
    • The graph will be in the first quadrant for x ≥ 0.

  2. Option #2: f(x) = 2√3√x

    • The expression seems unclear, as "2^3" can be interpreted as multiplying 2 by the cube root of x, which changes the shape significantly.
    • Without clear formatting, it’s hard to determine the exact nature of this option, especially since cube root functions also exist in both quadrants and can take negative values for negative inputs.

Based on the standard characteristics:

  • If the curve is mostly lying in the first quadrant and follows a smooth increasing trend from the origin (0,0), it likely matches Option #2, which describes a function with a square root, hence positively increasing and defined for non-negative x values.

Please verify the graph against these descriptions to determine the best match. If the curve shows a much steeper increase than a typical square root curve, Option #1 could be a candidate depending on the shape.