Question

Can someone explain/show me how to do this?Absolute Value Functions

Parent Function: f(x)=|x|
it asks for Characteristics:
Domain , Range, X-int, Y-Int
Increasing, decreasing
Then Transformations f(x) = f(x)=A|(x-B)| + C
A: B: C: -A:

Answer 1

Domain: -∞<x<∞
Range: -∞<x<∞
X-Intercept: x=0
Y-Intercept: y=0
Increasing on the interval of 0<x<∞
Decreasing on the interval of -∞<x<0


When A=0, the graph equals y=0
- When A is greater than 1, it makes the graph skinnier than f(x)=|x|
- When A is less than 1 but greater than 0, it makes the graph fatter than f(x)=|x|
- When A turns negative, it flips the graph upside down.

-When B is greater than 0, it translates the graph to the right
- When B is less than 0, it translates the graph to the left

When C is greater than 0, the graph moves upwards
When C is less than 0, the graph moves downwards