graph the equation shown below by transforming the given graph of the parent function. \n$y = \\sqrt{x} + 4$

Explanation:

Step1: Identify Parent Function

The parent function here is ( y = \sqrt{x} ), whose graph is shown (starting at (0,0), increasing slowly).

Step2: Analyze Transformation

The given function is ( y = \sqrt{x} + 4 ). This is a vertical shift transformation. For a function ( y = f(x) + k ), if ( k>0 ), the graph shifts up by ( k ) units. Here, ( k = 4 ), so we shift the graph of ( y = \sqrt{x} ) up 4 units.

Step3: Apply the Shift

• The vertex of ( y = \sqrt{x} ) is (0,0). After shifting up 4 units, the new vertex is (0, 0 + 4) = (0, 4).
• For other points, take a point on ( y = \sqrt{x} ), say (1,1). After shifting up 4, it becomes (1, 1 + 4) = (1, 5). Another point: (4,2) becomes (4, 2 + 4) = (4, 6), (9,3) becomes (9, 3 + 4) = (9, 7), etc.
• Then, plot these new points (0,4), (1,5), (4,6), (9,7) and draw the curve, which is the graph of ( y=\sqrt{x}+4 ), a vertical shift up 4 units from the parent square - root function.

Answer:

To graph ( y = \sqrt{x}+4 ), shift the graph of the parent function ( y=\sqrt{x} ) (with vertex at (0,0) and points like (1,1), (4,2), (9,3)) up 4 units. The new vertex is (0, 4), and other points are (1, 5), (4, 6), (9, 7), etc. Plot these points and draw the curve.