7 5 Graphing Square Root Cube Root Functions

7. 5 Graphing Square Root & Cube Root Functions

Objectives/Assignment • Graph square root and cube root functions • Assignment: 15 -49 odd

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) (4, 2) (9, 3) (-27, -3) (8, -6) (27, -9) (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 (x-value – 4) (y-value -1) Now, shift these points to the left 4 and down 1. x y 0 0 x y 1 2 -4 -1 4 4 -3 1 9 6 0 3 5 5

Graph (x-value + 3) (y-value + 2) Now, shift these points to the right 3 and up 2. x y -27 6 x y -8 4 -24 8 -1 2 -5 6 0 0 2 4 1 -2 3 2 8 -4 4 0 27 -6 11 -2 30 -4

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