6.5 Graph Square Root & Cube Root Functions

First, let’s look at the graphs. (27,3) (16,4) (8,2) (9,3)) (1,1) (4,2) (-1,-1) (-8,-2) (-27,-3) Think of these as “parent” functions.

Now, what happens when there is a multiplier in front of the radical? (16,8) (-27,9) (9,6) (8,2) (27,3) (4,4) (1,2) (16,4) (-27,-3) (9,3) (27,-9) (4,2) (8,-6) (1,1) Notice the “parent” has been “doubled” for each x-value. Can you guess what the graph of Notice the “parent” has “reversed” sign and tripled for each x-value.

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

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).

Describe how to obtain the graph of from the graph of Shift all the points from To the right 2 and up 1.

Graph Now, shift these points to the left 4 and down 1. x y 0 0 2 4 (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

Graph Now, shift these points to the right 3 and up 2. x y -27 6 -8 4 (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

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).