Graphing Square Root Parent Function
Please see the attached Parent Function Sheet. Remember to use all of our transformation rules regarding shifting left/right, up/down, stretch/shrink, and reflection.
8.7 Graphing Radical Inequalities
Ex 1:
Transformation is 5 units to the left. Graph as we did on the parent function.
Notice go over 1/up 1 (because the ), over 4/up 2 (because the ), and over 9/up 3(because the ).
****Now you must shade the inequality. Select a test point such as (0,-2). Be sure that the point is in the area of the domain where the inequality is defined. The point should not be on the curve.
Since the test is true, then the pt (0,-2) will be shaded.
Notice the shading stops at the vertical line x = -5 because that is where the function becomes undefined.
Also, notice that the curve is broken because it is < not
The domain is and the range is . Yes, the upper bound on the range here is infinity because as the graph continues out for large values of x, the y values continue to increase.
Ex. 2
There is no horizontal transformation but there is a vertical stretch of 3 and a reflection over the x axis.
Start at the origin because there is no horizontal or vertical translation.
Notice go over 1/down 3 (because the ), over 4/down 6 (because the ), and over 9/down 3(because the ). Don’t forget the STRETCH. Yes, the point (0,0) is the “starting point”.
EX 3: Describe the transformation of the parent function if.
Translated Right 2 and Up 2
EX 4:
This is a solid curve due to the greater than or EQUAL.
It has been translated right 1.
Worry about graphing the square root first. Then worry about the shading.
Domain: and Range:
EX 5: The speed in miles per hour of a tsunami can be modeled by the function , where d is the average depth in feet of the water over which the tsunami travels. Use this function to predict the speed of a tsunami over water with a depth of 1500 feet.