7.5 Graphing Square Root & Cube Root Functions

7.5 Graphing Square Root & Cube Root Functions p. 431

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 If a > 1, Then the graph stretches. If 0< a < 1, Then the graph shrinks. 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) The Negative Reflects the graph About the x axis.

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.

Ex: Graph (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

Ex: Graph (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 • 0 • -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).

Assignment

7.5 Graphing Square Root & Cube Root Functions