In the previous section, you generated tables of square root functions from algebraic and verbal descriptions. In this section, you will focus your attention toward generating graphs. Graphs allow you to see the defining characteristics of the function family. Graphs also allow you to be able to easily determine attributes such as domain, range, and the coordinates of the endpoint. Creating a graph using a graphing calculator is pretty easy. You type the equation into the function editor, usually the Y = menu, and press GRAPH. However, creating a graph by hand takes a little thought. Review the example below.

Given y = √(3x + 4), make a table of values to represent this equation. The first row is completed for you. Drag and drop the remaining processes and y-values to complete the table.

Now that the equation is in the form of a table, you can plot these points on a coordinate plane. Click on the graph below to plot the points and graph the function.

Conclusion Questions

• Looking at the graph, what are the coordinates of the endpoint of the graph?

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  Check Your Answer

  

• What is the domain and range?

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  Domain {x | x ≥ - 4 over 3 4 3 }; Range {y | y ≥ 0}

• Looking at the graph, approximate the value of y if x = 2.

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  It looks like at x = 2, y would be a little more than 3. Estimate y to equal about 3.2.

Pause and Reflect

You have been generating graphs from tables and algebraic representations.

Above is a graph of a square root function. What is the algebraic equation for this graph? Explain how you determined the equation.

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Check Your Answer

The equation is y = √(x + 6) – 3. You find this by determining the transformation. The graph is shifted to the left 6 units and down 3 units from the parent function.

What are the coordinates of the endpoint?

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Check Your Answer

(−6, −3)

Practice

1. Which graph represents f(x) = √(3x + 3) ?
   

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   Determine the value of x that makes the number under the radical sign equal to zero.

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   Check Your Answer

   C

2. What are the coordinates of the endpoint for the function graphed below?
   

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   Find the starting point on the graph.

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   (0, 3)

3. Identify the domain and range for the graph in practice problem 2.

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   Use the coordinates of the endpoint to determine the domain and range.

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   Check Your Answer

   Domain {x | x ≥ 0}; Range {y | y ≥ 3}