Download 2.6A Absolute Value Functions (Graph Calc)

Algebra 2
2.6A Absolute Value Functions
Obj: able to find the vertices of absolute value functions and graph them using a calculator.
Recall the definition of absolute value from Chapter 1:
The absolute value of a number is ___________________________________________.
absolute value function – the function f(x) = | x |, or in linear equation format, y = | x |. This is a ‘V’ shaped graph
where the point of the ‘V’ is called the vertex.
finding the vertex of an absolute value function – let the expression inside the absolute value bars equal zero and
solve for x. This x value is then the x-coordinate of the vertex. Once you know the value for x, use it in the linear
equation format to find the value for y, which will be the y-coordinate of the vertex.
1.
Find the vertex of the function y = | x | . Then complete the table and graph the function.
Let x = 0, then | x |=0, and y= | 0 |, putting the vertex at (0, 0).
vertex
2.
x
-2
-1
0
1
2
y
0
Find the vertex of the function y = | x | + 1. Then complete the table and graph the function.
Let x = 0, then | x |=0, and y= | 0 | + 1, putting the vertex at (0, 1).
vertex
3.
x
-2
-1
0
1
2
y
1
Find the vertex of the function y = | x + 1 | . Then complete the table and graph the function.
Let x + 1= 0, then x = -1 makes | x + 1 |=0, and y= | 0 | , putting the vertex at (-1, 0).
vertex
x
-2
-1
0
1
2
y
0
2.6A Cooperative Learning
DIRECTIONS: With your partner, work out the following problems. You both need to record answers on your
own page as you work together.
Graphing Absolute Value Functions on the TI-83+
In the Y= screen, type in the equation y1 = | x | . To make the absolute value bar, press MATH, ► (NUM menu) and then 1:
abs( . This takes you back to the Y= screen, so press X,T,Θ,n to enter the x variable, and then make sure to close off the
absolute value by adding in the close parentheses ). Press ZOOM , 6: ZStandard to set the window at the standard 10 units
nd
in each direction from the origin and to see the graph. Press 2 , GRAPH to see a table of ordered pairs (x, y1) and (x, y2)
for each of the functions
Graph each pair of equations on a graphing calculator. Then sketch the pair on the same graph and label by problem #.
1.
y1 = | x |
2. y2 = 2| x |
7.
y1 = 3| x |
8. y2 = -3| x |
3. y1 = | x | + 2
4. y2 = | x | – 3
5. y1 = | x + 2 |
6. y2 = | x – 4 |
The parent graph for absolute value functions is y = | x | with a vertex at (0, 0)
A vertical translation occurs when y = | x | ± k, where k is a positive number.
y = | x | + k translates the graph of the parent function _________ k units.
y = | x | – k translates the graph of the parent function _________ k units.
A horizontal translation occurs when y = | x ± h |, where h is a positive number.
y = | x + h | translates the graph of the parent function _________ h units.
y = | x – h | translates the graph of the parent function _________ h units.
A combined translation occurs when y = | x ± h | ± k, where h and k are positive
A stretch occurs when y = a| x ± h | ± k and a > 1
A reflection about the x-axis occurs when y = a| x ± h | ± k and a < 0
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