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Which graph accurately demonstrates the relationship between the functions f(x)=x−−√

and f(x)=x−−√+3
?(1 point)
Responses

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
Image with alt text: Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
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a b c or d

1 answer

To identify which graph accurately demonstrates the relationship between the functions \( f(x) = \sqrt{x} \) and \( f(x) = \sqrt{x} + 3 \), we should analyze their characteristics:

  1. The function \( f(x) = \sqrt{x} \):

    • This function is defined for \( x \geq 0 \) and produces non-negative values.
    • The graph starts at the origin (0,0) and increases gradually.

  2. The function \( f(x) = \sqrt{x} + 3 \):

    • This function is also defined for \( x \geq 0 \) and produces values that are shifted upwards by 3 compared to the first function.
    • The graph starts at (0,3) instead of (0,0) due to the vertical shift.

Given these characteristics, the graph of \( f(x) = \sqrt{x} \) will be below the graph of \( f(x) = \sqrt{x} + 3 \) for all \( x\) in the domain. Also, both graphs will only exist where \( x \) is greater than or equal to 0.

Now, looking at your provided options:

  • The selection will be determined by whether the graphs clearly demonstrate that one is the other shifted up by 3 units, with both graphs starting from the non-negative section of the x-axis.

Since no specific graph images are provided here, you should look for the following in the correct option:

  • Ensure one curve starts at (0,0) and gradually rises.
  • The second curve should start at (0,3) and also rise, maintaining the same shape as the first curve but shifted up.

Therefore, any graph that meets these criteria would correctly represent the two functions. However, since the exact images aren't viewable, please select the graph that reflects this analysis and presents both functions accurately plotted.