Library+of+Functions-Target+B-Graphing+Abs-Guided+Learning

Library of Functions-Target B: Graph and Compare Absolute Value Functions

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The parent or reference function for absolute value functions is: math f(x)=|x|\ math

The reference function is the most basic absolute value function, with an "a" value of 1, and the vertex (h, k) located at the origin (0, 0).

When comparing absolute value functions to the reference function, we need to look at what the a, h, and k values do to the graph of the functions. Use the applet below to explore the changes that occur between absolute value functions and their graphs. Use the questions below to help guide your exploration. media type="custom" key="26404304" Use the slider to change the value of a. What happens to the graph of the function as "a" becomes larger? Smaller? What happens when "a" is a negative number? Use the slider to change the value of h. How does the graph change as "h" changes? Use the slider to change the value of k. How does the graph change as "k" changes?


 * Comparing Absolute Value Functions** When comparing absolute value functions, there are 3 main ideas to consider. When you are describing the differences between an absolute value function to the reference function, you always want to keep in mind the values of the a, h, and k, and the roles they play in the shifts of the graph. Use the following descriptions to compare absolute value functions.

"a" value:
 * if |a| > 1, stretched
 * if 0 < |a| < 1, compressed
 * if a is positive: opens up
 * if a is negative: opens down

"h" value:
 * if adding an h value: vertex translates to the left
 * if subtracting an h value: vertex translates to the right

"k" value:
 * if adding a k value: vertex translates up
 * if subtracting a k value: vertex translates down

Compare the following functions to the reference function f(x) = |x|:
 * Examples:**

g(x) = 3|x + 5| - 1 h(x) = 2/3|x| + 4 k(x) = -2|x - 7|

For g(x) = 3|x + 5| - 1: So the graph of g(x) opens up, is stretched, and is translated left and down in comparison to the graph of f(x).
 * "a": positive 3, so the graph would OPEN UP and be STRETCHED since the absolute value of 3, |3|, is greater than 1
 * "h": adding a 5 so the graph would be TRANSLATED to the LEFT 5 units
 * "k": subtracting a 1 so the graph would be TRANSLATED DOWN 1 unit

For h(x) = 2/3|x| + 4 So the graph of h(x) opens up, is compressed, and is translated up in comparison to the graph of f(x).
 * "a": postive 2/3, so the graph would OPEN UP and be COMPRESSED since the absolute value of 2/3, |2/3|, is between 0 and 1
 * "h": there is no h inside the absolute value so the graph would not be translated to the left or right
 * "k": adding a 4 so the graph would be TRANSLATED UP 4 units

For k(x) = -2|x - 7| So the graph of k(x) opens down, is stretched, and is translated right in comparison to the graph of f(x).
 * "a": negative 2, so the graph would OPEN DOWN, and be STRETCHED since the absolute value of -2, |-2|, is greater than 1
 * "h": subtracting an h so the graph would be TRANSLATED to the RIGHT 7 units
 * "k": there is no k being added or subtracted after the absolute value so the graph would not be translated up or down

1) Compare the graph of the function j(x) = -|x + 4| + 8 to the graph of the reference function f(x)= |x|. 2) Write an absolute value function that has the following characteristics: opens up, compressed, and is translated to the left and down.
 * Library of Functions-Target B-Graphing Abs-Quick Check:**

Library of Functions-Target B-Graphing Abs-Quick Check Solutions