7.5 Graphing Square Root & Cube Root Functions

What do the graphs of and look like? What is the standard equation for a square root or cube root whose center has been translated? How do you graph a square root function? How do you graph a cube roof function? What is domain & range?

First, let’s look at the parent graphs.

Now, what happens when there is a number in front of the radical? * Notice the graph goes thru the points (0,0) and (1,2). * Notice the graph goes thru the points (-1, 3), (0,0), & (1,-3).

Generalization Always goes thru the points (0,0) and (1,a). Always goes thru the points (-1,-a), (0,0), and (1,a).

Ex: Graph Goes thru the points (0,0) and (1,a). Since a=-4, the graph will pass thru (0,0) and (1,-4)

Now, what happens when there are numbers added or subtracted inside and/or outside the radical? Step 1: Find points on the parent graph Step 2: Shift these points h units horizontally (use opposite sign) and k units vertically (use same sign).

Ex: Describe how to obtain the graph of from the graph of Shift all the points from To the right 2 and up 1. (−1+2, 1+1) (0+2,0+1) (1+2,1+1) (1,2) (2,1) (3,2)

Ex: Graph Now, shift these points to the left 4 and down 1. x y 0 0 2 (x-value – 4) (y-value -1) Now, shift these points to the left 4 and down 1. x y 0 0 2 4 9 6 x y -4 -1 -3 1 0 3 5 5

Or…Just Graph by picking values x y -4 -1 -3 1 0 3 5 5

Ex: Graph Now, shift these points to the right 3 and up 2. x y -27 6 (x-value + 3) (y-value + 2) Now, shift these points to the right 3 and up 2. x y -27 6 -8 4 -1 2 0 0 -2 -4 27 -6 x y -24 8 -5 6 4 2 -2 30 -4

Or…just graph By picking values that will combine to make the value under the radical a real number using the 3rd root. x y -24 8 -5 6 4 2 -2 30 -4

Ex: State the domain and range of the functions in the last 2 examples. x-values y-values Domain: Range: Domain: Range: The graph doesn’t have a beginning or ending point. (Meaning all x & y-values are possible.) The graph has a beginning point of (-4,-1).

Helpful Hints (h,k) is where the graph will begin. (h,k) is where the graph will change directions.

What do the graphs of and look like? Half of a parabola and a s-shaped graph. What is the standard equation for a square root or cube root whose center has been translated? How do you graph a square root function? Find the new beginning point from (h,k) and then pick points to plot. How do you graph a cube roof function? Find the new center point from (h,k) of the S curve and then pick points to the left and to the right to plot. What is domain & range? Domain are the x values for the graph and the range are the y values for the graph

Assignment Page 434, 15-21, 22-44 even