Graphic Square Root Functions

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To chart a square root function, follow these steps:

  1. The function should be written in the form y = a√x + b, where a and b are constants.
  2. Plot the y-intercept of the function, the point where the graph intersects the y-axis. This point is given by (0, b).
  3. Define the range and function of the domain. The set of all x-values for which the function is defined is known as the domain of a square root function. The domain in this instance is x ≥ 0. The set of all y-values that the function accepts constitutes its range.
  4. Connecting the plotting points and a smooth curve will help in creating the graph of the function. To plot points, you can change the value of x in the function and then reach the solution for y. For instance, you can apply the function with x = 1 and then crack the solution for y to get y = 2 to plot the points (1, 2).
  5. If the coefficient an is positive, the graph opens ‌upward and will cross the x-axis at x = 0. If the coefficient a is negative, the graph opens downwards and will not cross the x-axis.
  6. The graph will move upwards from the y-axis if the constant b is positive. The graph will move downwards from the y-axis if b is negative.

Find an example of how to chart the function y = √x + 2:

  1. Write the function in the form y = a√x + b, where a and b are constants. Here, a = 1 and b = 2.
  2. Plan the y-intercept of the function, the point (0, 2).
  3. Resolve the range and domain of the function. The domain is x ≥ 0 and the range is y ≥ 2.
  4. Plot points on the graph and connect them with a curved line to create the function's graph. As an example, you can plan the points (1, 2), (4, 3), and (9, 4).
  5. The graph opens upwards and crosses the x-axis at x = 0.

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