1. Graphing absolute value functions and transformations
Math 2: Unit 5B Day 2
Graphing absolute value functions and transformations

2. Absolute Value Parent Function

3. Transformations and translations of the parent function
The graph has vertex (h,k) and is symmetric in the line x = h
h shifts the parent function horizontally (remember to change the sign)
k shifts the parent function vertically
The graph is V-shaped.
It opens up if a > 0 and down if a < 0.
The graph is wider than the graph of if
< 1 and narrower if >1.

4. Transformations and translations of the parent function

5. Identify the vertex, tell whether the graph opens up or down, then tell whether the graph is wider or narrow or normal compared to
Vertex (-3,-5),
opens up,
Narrower.
Vertex (0,-5),
opens up,
Wider.

6. Identify the vertex, tell whether the graph opens up or down, then tell whether the graph is wider or narrow or normal compared to
Vertex (5,-2),
opens down,
Narrower.
Vertex (½,4),
opens up,
Normal or the same.
Vertex (5,0),
opens down,
Normal or the same.

7. Intercepts To find the x-intercept(s): substitute in 0 for y
To find the y-intercept: substitute in 0 for x
From a graph, the intercepts are where the graph crosses each axis.
No x-intercepts!
y-intercept (0,-2)

8. Domain and Range Domain (x-values): read from left to right
Range (y-values): read from bottom to top
Find the domain and range
of this function.
Domain: all real numbers
Range: y ≥ 2.

9. Domain and Range Domain (x-values): read from left to right
Range (y-values): read from bottom to top
Find the domain and range
of this function.
Domain: all real numbers
Range: y ≥ - 4 .

10. Domain and Range Domain (x-values): read from left to right
Range (y-values): read from bottom to top
Find the domain and range
of this function.
Domain: all real numbers
Range: y ≤ - 1 .

11. Zeros The values of x when f(x) = 0
To find the zeros of any function: plug in y = 0 and solve for x.
Find the zero(s) of
x = -1 and x = 3 .

12. Intervals of increasing and decreasing
Find the intervals where this function is increasing
and decreasing.
Decreases:
Increases:
Decreases: (-∞, -3)
Increases: (-3,∞)

13. Intervals of increasing and decreasing
Find the intervals where this function is increasing
and decreasing.
Decreases:
Increases:
Decreases: (-∞, 2)
Increases: (2,∞)

14. Intervals of increasing and decreasing
Find the intervals where this function is increasing
and decreasing.
Decreases:
Increases:
Increases: (-∞, -2)
Decreases: (-2,∞)

15. Graphing To graph an absolute value function
Find the vertex and sketch the AOS
Use a table of values choosing 2 x-values on each side of the vertex
plot the points and draw the graph

16. Graphing Vertex: Max/min? Axis of symmetry: Domain: Range:
Y-intercept:
Zeros:
Intervals of increase and decrease
( - 2, - 1)
minimum
x = - 2
all real numbers
y ≥ - 1 .
( 0, 1)
( -3, 0) and ( -1, 0)
Decreases: (-∞, -2)
Increases: (-2,∞)

17. Graph the following: Vertex: Max/min? AOS: Domain: Range: Intercepts:
Zeros:
Intervals of increase and decrease x y

18. Graph the following: Vertex: AOS: Domain: Range: Intercepts: Zeros:
Intervals of increase and decrease x y

19. Graph the following: Vertex: Max/min? AOS: Domain: Range: Intercepts:
Zeros:
Intervals of increase and decrease x y

20. Slope is the average rate of change!
Calculating average rate of change
Do you remember how to find slope when given 2 points?
If you know any two points on a line, or two solutions of a linear equation, you can find the slope of the line without graphing.
Slope is the average rate of change! 20

21. On the following graph, where is the rate of change positive
On the following graph, where is the rate of change positive? Where is it negative?
Tell about the interval:

22. On the following graph, where is the rate of change positive
On the following graph, where is the rate of change positive? Where is it negative?
Tell about the interval:

23. Assignment:
Handout