Translating Absolute Value Functions
- Author:
- mrvettleson
- Topic:
- Translation
Below is the Equation y=a|x-b|+c. Translations of the parent equation y=|x| by changing the values of a, b and c.
Set a=1, b=0, and c=0. This will graph the parent function y=|x| having a vertex at the origin (0,0).
1. Leaving a=1 and c=0.
a. How does changing the value of b effect the parent function y=|x|.
i. To 3?
ii. To 5?
iii. To -3?
iv. To -5?
2. Leaving a=1 and b=0.
a. How does changing the value of c effect the parent function y=|x|.
i. To 3?
ii. To 5?
iii. To -3?
iv. To -5?
3. Leaving b=0 and c=0.
a. How does changing the value of a effect the parent function y=|x|.
i. To 3?
ii. To 4?
iii. To .5?
iv. To -.5?
v. To -2?
vi. To -3?
b. How does the parent function change when a>0 (a is greater than 0)?
c. How does the parent function change when 0<a<1(a is between 0 and 1)?
d. How does the parent function change when a<0(a is less than 0)?
4. Set a=.5, b=3, c=-2 and explain the transformation of the parent function.
5. What is the absolute value equation that has a vertex shifted 3 units right, 2 units down, is reflected across the x-axis (looks upside down), and stretched by a scale factor of 3.