1. 1.4 – Shifting, Reflecting, and Stretching Graphs

2. In this section, you will learn to:
identify unit graphs of various functions
transform a unit graph by stretching, shifting and reflecting
write the equation of a transformed graph using the sketch of the graph

3. Common Unit Graphs:
1) Constant Function:

4. Common Unit Graphs:
2) Linear Function:

5. Common Unit Graphs:
3) Absolute Value Function:

6. Common Unit Graphs:
3) Absolute Value Function:

7. Common Unit Graphs:
4) Quadratic Function:

8. Common Unit Graphs:
4) Quadratic Function:

9. Common Unit Graphs:
5) Square Root Function:

10. Common Unit Graphs:
5) Square Root Function:

11. Common Unit Graphs:
6) Cubic Function:

12. Common Unit Graphs:
6) Cubic Function:

13. Common Unit Graphs:
7) Rational Function:

14. Common Unit Graphs:
7) Rational Function:

15. Summary of Graphing: Rigid Transformations: Shape/size do not change
a) Vertical shift c units upward:

16. Summary of Graphing: Rigid Transformations:
b) Vertical shift c units downward:

17. Summary of Graphing: Rigid Transformations:
c) Horizontal shift c units to the right:

18. Summary of Graphing: Rigid Transformations:
d) Horizontal shift c units to the left:

19. Summary of Graphing: Rigid Transformations:
e) Reflection across the x-axis:

20. Summary of Graphing: Rigid Transformations:
f) Reflection across the y-axis:

21. Summary of Graphing: Non-Rigid Transformations: Shape/size will change
a) Vertical stretch by c units if c > 1 :

22. Summary of Graphing: Non-Rigid Transformations:
b) Vertical shrink by c units if 0 < c < 1:

23. Graphing Examples: Describe the transformation of the following
Function:
This is an absolute value function shifted
a) 4 units to the right
b) 6 units up
c) reflection across the x-axis
d) vertical shrink

24. Graphing Examples:

25. Y-Axis Reflection Graphing Examples:

26. Graphing Examples: Write a cubic equation with the following
transformations:
a) 3 units to the left
b) 2 units down
c) reflection across the x-axis
d) vertical stretch

27. Graphing Examples:

28. Writing an Equation:
Write the equation of the graph below.

29. Writing an Equation:
Write the equation of the graph below.

30. Writing an Equation: 3 units right 2 units up x-axis reflection
Write down the transformations.
3 units right
2 units up
x-axis reflection
Use (4,1) as a point on the graph

31. Writing an Equation:
Write the quadratic equation of the graph below.

32. Writing an Equation: The graph has been reflected across the x-axis.
The vertex has been translated 1 unit to the right and 1 unit up. This represents (h,k).
The graph has been reflected across the x-axis.
Use one point on the graph, the vertex and solve for the value of a for the quadratic equation

33. Writing an Equation: One point on the graph is Solve for a.
The vertex is (h,k) which is (1,1).
One point on the graph is
Solve for a.

34. Writing an Equation:
Sketch the graph of f(x+1) given the following function.

35. Writing an Equation:
Sketch the graph of f(x)-3 given the following function.

36. Writing an Equation:
Sketch the graph of f(-x) given the following function.

37. Writing an Equation:
Sketch the graph of - f(x)+1 given the following function.

38. Writing an Equation:
Sketch the graph of 2f(x)-1 given the following function.