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Input. Output. 2 5 -1 6. 3 -2. Domain = -1, 2, 5 & 6 Range = -2 & 3. 7.8 Warm-Up. 2) Graph y = -2x 2 + 3. 1) Identify the domain and range. Objective- Students will learn to graph functions of the form y = a x – h + k and y = a 3 x – h + k. y. y. (1,1). (1,1). - PowerPoint PPT Presentation
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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