Simplify the Following Radicals

Wednesday March 12 th

 A square root function is a function containing a square root with the independent variable in the radicand.  The easiest way to graph a function is to create an x and y table. Graph y = xy

 Now when you are graphing square roots there is no need for you to include negative x values in your table.  Remember taking the square root of a negative number creates no real roots, so you will be unable to graph non-real roots.  So to find what number to start with we need to find the x-value that will give you a real number answer

Set the radicand equal to zero. Solving will provide us with the start value. For example what if we had We would set x – 2 = 0 and solve for x. Radicand

 To complete the x/y table, we need to decide where to start.  Do you remember how to calculate the starting x-value?  Set the RADICAND equal to 0.  x + 7 = 0, Start with x = -7

Given the Radicand: Set up an inequality showing the radicand is greater than or equal to 0. Solve for x. The result is your DOMAIN!

Domain:Range: xy xy

Domain:Range: xy xy

Domain:Range: xy xy

Domain:Range: xy xy

 We are going to look back at the graphs we made and compare/contrast the similarities and differences among their graphs and functions.

What is different about the graphs? How did the 2 nd graph “shift”? xy xy

When you ADD or SUBTRACT under the radical, you shift in the opposite direction. xy

xy xy When you DIVIDE or MULTIPLY under the radical, the graph is STRETCHED out side to side or COMPRESSED.

When you ADD or SUBTRACT outside of the radical, you shift UP or DOWN. xy xy

1. Subtract under the radical 2. Add under the radical 3. Multiply under the radical 4. Divide under the radical 5. Add outside of the radical 6. Subtract outside of the radical a) Move up b) Move right c) Move down d) Move left e) Stretch f) Compress

Check the 1 st and 3 rd lines in your calculator. Do they match?

 Parent Function: xy

 Subtract under the radical  Add under the radical  Multiply under the radical  Divide under the radical  Add outside of the radical  Subtract outside of the radical

 Worksheet

 By definition, absolute value is the distance from zero.  Can we ever have a negative distance?  How far away from zero is 3?  How about -2?

 How many ways are there to be 4 units away from zero?

 Evaluating an absolute value expression still requires PEMDAS. We treat absolute value bars like parenthesis, so we want to simplify inside of the bars first.  Example: Evaluate when x = 1.

Why do you think the graph looks like this?

 Domain:  Range:

 This will always give us the basic shape of our absolute value functions. We will use what we know about transformations to shift the graph.

 Based on what happened to radicals, describe the transformations that might occur for each of the following from the parent function:

 Add/Subtract INSIDE the bars:  opposite direction, left and right  Multiply by a value greater than 1 in FRONT:  stretch (skinny), slope of right side  Multiply by a value between 0 and 1 in FRONT:  wider, slope of right side  Add/Subtract after the bars:  up and down

 To graph absolute value functions with transformations, we want to look from left to right. We will graph the transformations in that order.

 Domain:  Range:

 Domain:  Range:  Domain:  Range:

 Worksheet