Do Now: If you have progress reports, put them in my basket Tell the transformations by looking at the following equations: y = -2(x – 3)2 +5 y = 8(x + 1)3 – 9 Midterm Review:

Graphs of Radical & Cube Root Functions Domain, Range, & Shifts

Graphing Square Root Functions 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 = x y 1 2 4 9

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

Radicand 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.

Graphing Radical Functions 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

Determine the start values

Domain of a Radical Function 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!

Determine the DOMAIN

Radical Parent Functions

Graph the function x y x y Domain: Domain: Range: Range: What is different about the graphs? How did the 2nd graph “shift”? x y x y

Graph the function Domain: Domain: Range: Range: x y x y

Graph the function Domain: Domain: Range: Range: x y x y

Graph the function Domain: Domain: Range: Range: x y x y

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

Graph the function When you ADD or SUBTRACT under the radical, you shift in the opposite direction. x y 4 5 1 8 2 13 3 20

x y .5 1 2 4.5 3 8 4 x y 1.5 1 3 2 13.5 24 4 When you DIVIDE or MULTIPLY under the radical, the graph is STRETCHED Horizontally out side to side or COMPRESSED Horizontally.

Graph the function When you ADD or SUBTRACT outside of the radical, you shift UP or DOWN. x y 3 1 4 5 9 6 16 7 x y -5 1 -4 4 -3 9 -2 16 -1

Recap Radical Shifts Matching Subtract under the radical Move up Add under the radical Move right Multiply under the radical Move down Divide under the radical Move left Add outside of the radical Stretch vertically Subtract outside of the radical Compress vertically

Radical Transformations… Moving radical functions around the graph… What do you notice about the placement of each letter compared to their transformation? (think, what did we talk about yesterday and how did each letter in the equation transform the function?

Radical Transformations

Transformations We apply the transformations on these functions in the same manner as we did with the polynomial functions. Vertical stretch of 3 Vertical shift up 2 Horizontal shift right 3

Try these… Vertical stretch 3 Horizontal shift left 1 Vertical shift down 1 Reflect @ x-axis Vertical shift up 4 Horizontal shift right 2 Vertical shrink of ½

Try these… Vertical stretch of 3 Horizontal shift left 2 Vertical shift down 4 Reflect @ x-axis Vertical shrink of ½ Horizontal shift right 1 Vertical shift up 2

We simplify the radicand if possible Check the 1st and 3rd lines in your calculator. Do they match?

Graphing a Cubed Root Function Parent Function: Domain: Range: x y 1 2 4 9

How do Cubed Roots Move?

Cubed Root Transformations 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

You Try – sketch the graphs of each of the following and give their domain and range: x y x y x y

You Try – sketch the graphs of each of the following and give their domain and range: x y x y x y

NC Final Exam Question

Solving Square Root Functions

Homework: Worksheet