1. Warm-up: Welcome Ticket
Translating Functions WKS

2. HW Key: p. 101: 48, 50, 52

3. HW Key: p. 101: 48, 50, 52
50) 52)

4. 2.3 Stretching, Shrinking, & Reflecting Graphs
Unit 2
2.3 Stretching, Shrinking, & Reflecting Graphs

5. Objectives & HW
The students will be able to stretch or shrink a parent function vertically and horizontally, and reflect graphs across the x- and y-axes.
HW: p. 111: 2, 4, 6, 8, 14, 16, 18

6. Reflecting Across the x- or y-axis:
Graph the following on the same set of axes: ● ● ●

7. Reflection Rules:
Graph is reflected across the x-axis.
Graph is reflected across the y-axis.

8. 2.3 Example of Reflection Given the graph of sketch the graph of
(a) (b)
Solution
(a) (b)

9. Vertical Stretch and Compression:
Graph the following on the same set of axes: ● ● ●

10. Vertical Stretch and Compression Rules:
If c > 1, the graph stretches vertically by a factor of c.
If c < 1, the graph compresses vertically by a factor of c.

11. Horizontal Stretch and Compression:
Graph the following on the same set of axes: ● ● ●

12. Horizontal Stretch and Compression Rules:
If c > 1, the graph compresses horizontally by a factor of 1/c.
If c < 1, the graph stretches horizontally by a factor of 1/c.

13. Combining Transformations of Graphs
Example
Describe how the graph of can be obtained by transforming the graph of Sketch its graph.
Solution
Since the basic graph is the x-coordinate of the vertex of the parabola is shifted right 4 units. Since the coefficient of is –3, the graph is stretched vertically by a factor of 3 and then reflected across the x-axis. The constant +5 indicates the vertex shifts up 5 units.
shift 4 units right
shift 5 units up
vertical stretch by a factor of 3
reflect across the x-axis

14. Identify the parent function that can be used to graph each function
Identify the parent function that can be used to graph each function. Do not graph the function.
1) g(x) = 4|x| - 3
1) f(x) = |x|

15. Write a rule for the function whose graph can be obtained from the given parent function by performing the given transformations.
1) parent function: f(x) = x3
transformations: shift the graph 7 units to the left and upward 5 units
1) f(x) = (x + 7)3 + 5

16. Write a rule for the function whose graph can be obtained from the given parent function by performing the given transformations.
2) parent function: f(x) = |x|
transformations: shift the graph 4 units to the right, stretch it vertically by a factor of 3, and shift it down 2 units.
2) f(x) = 3|x – 4| – 2

17. Describe the sequence of transformations that transform the graph of the parent function f into the graph of the function g. Do not graph.
3) f(x) = x2 g(x) = 0.25(x – 6)2 + 3
3) Shift the graph 6 units to the right and 3 units up, then compress it vertically by a factor of 0.25.

18. Closure
Using the following scale:
3: I totally understand this.
2: I sort of understand this.
1: I am clueless.
Rate the following:
Vertical and Horizontal Stretches and Compressions
Finding the parent graph
Describing the transformation given the graph
Writing the equation given the transformations