1) Identify the domain and range

Input Output

2

5

-1

6

3

-2

2) Graph

y = -2x2 + 3

Domain = -1, 2, 5 & 6

Range = -2 & 3

x

y

x

y

Domain: x > 0, Range: y > 0 Domain and range: all real numbers

(0,0)

(1,1) (1,1)

(0,0)(-1,-1)

Objective- Students will learn to graph functions of the form y = a x – h + k and y = a 3 x – h + k.

Example 1

Describe how to create the graph of y = x + 2 – 4 from the graph of y = x .

Comparing Two Graphs

Solution

h = -2 and k = -4

shift the graph to the left 2 units & down 4 units

Graphs of Radical Functions

To graph y = a x - h + k or y = a 3 x - h + k, follow these steps.

STEP Sketch the graph of y = a x or y = a 3 x .

STEP Shift the graph h units horizontally and k units vertically

Example 2

Graph y = -3 x – 1 + 3 .

Graphing a Square RootSolution

1) Sketch the graph ofy = -3 x (dashed).It begins at the origin and passes through point (1,-3).(1, 3)

(1,-3)

(0,0) (2,0) 2) For y = -3 x – 1 + 3, h = 1 & k = 3.

Shift both points 1 to the right and 3 up.

Graph y = 2 x – 2 + 1 .

Graphing a Square Root

(2, 1)(1,2)

(0,0)

(3,3)

Graph y = 2 3 x + 3 – 4 .

Example 3Graphing a Cube Root

Solution

1) Sketch the graph of y = 2 3 x (dashed).It passed through the origin & the points(1, 2) & (-1, -2).

(-4,-6)

(0,0)

(-3,-4)

(-2,-2)(-1,-2)

(1, 2)

2) For y = 2 x + 3 – 4, h = -3 & k = -4.

Shift the three points Left 3 and Down 4.

Graph y = 3 3 x – 2 + 1

Graphing a Cube Root

(1,-2)

(0,0) (2,1)

(3,4)

(-1,-3)

(1, 3)

Pg. 423# 1 – 23* odd

Pg. 423 # 3 – 6 and 18 – 21