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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 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.

1 answer

To determine which graph accurately demonstrates the relationship between the functions f(x) = √x and f(x) = √x + 3, let's analyze the two functions.

  1. Function f(x) = √x:

    • The square root function starts at the origin (0,0) for x = 0 and is defined for x ≥ 0.
    • As x increases, the function increases slowly and goes upwards indefinitely.

  2. Function f(x) = √x + 3:

    • This function is the same as the first but shifted vertically upwards by 3 units.
    • It still starts at point (0,3) when x = 0 and continues to increase as x increases.

Now, looking for the correct graph:

  • The first function starts at (0,0) and the second function starts at (0,3).
  • Therefore, we expect to see two curves where one is below the other (specifically, the second curve being above the first curve).

From the options provided, we need to remember that the second function does not output values lower than 3 while the first function starts from 0.

Both functions only map to the domain of x ≥ 0, so the x-axis should start from 0.

  • If we look for a graph that has oscillating values in the y-axis, one set would be positive values for both curves, with the second curve (√x + 3) offsetting the first one by +3.

Without seeing the actual options, I would suggest selecting a graph that meets the criteria:

  • The first graph touches or starts from (0,0).
  • The second curve intersects or starts from (0,3).
  • The y-values of the second curve should consistently be above the first by 3 units.

Based on the provided descriptions, I cannot definitively tell which option is correct. You should select a graph that meets the criteria above relating to the provided details of the curves. If both curves have points indicated where they range correctly and the y-axis shown allows for those values, it would be an approximation based on definitions.

If you have access to any graph formats or specifics, please refer back to those evaluation points!