Create a piecewise definition for the given absolute value function.
Problem 1 :
f(x) = |x + 1|
Solution :
f(x) = |x - 1|
f(x) = x - 1 and f(x) = -(x - 1)
Case 1 :
f(x) = x - 1
when x ≥ 1, f(x) is positive
Case 2 :
f(x) = -(x - 1)
when x < 1, f(x) is negative
Distributing negative, we get
f(x) = - x + 1
So, the required definition is
Problem 2 :
f(x) = |x - 4|
Solution :
f(x) = |x - 4|
f(x) = x - 4 and f(x) = -(x - 4)
Case 1 :
f(x) = x - 4
when x ≥ 4, f(x) is positive
Case 2 :
f(x) = -(x - 4)
when x < 4, f(x) is negative
Distributing negative, we get
f(x) = - x + 4
So, the required definition is
Problem 3 :
f(x) = |4 - 5x|
Solution :
f(x) = |4 - 5x|
f(x) = 4 - 5x and f(x) = -(4 - 5x)
Case 1 :
f(x) = 4 - 5x
when x < 4/5, f(x) is positive
Case 2 :
f(x) = -(4 - 5x)
when x ≥ 4/5, f(x) is negative
Distributing negative, we get
f(x) = - 4 + 5x
So, the required definition is
Problem 4 :
f(x) = |3 - 2x|
Solution :
f(x) = |3 - 2x|
f(x) = 3 - 2x and f(x) = -(3 - 2x)
Case 1 :
f(x) = 3 - 2x
when x < 3/2, f(x) is positive
Case 2 :
f(x) = -(3 - 2x)
when x ≥ 3/2, f(x) is negative
Distributing negative, we get
f(x) = - 3 + 2x
So, the required definition is
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM