Question

Given the following absolute value function sketch the graph of the function and find the domain and range.

Answer 1

f(x) = 2|-4x + 5| - 4

Solution to Example 3

The range of |-4x + 5| is given by 

|-4x + 5| ≥ 0 

Multiply both sides of the inequality by 2 to obtain 

2 |-4x + 5| ≥ 0 

Add -4 to both sides of the above inequality to obtain 

2 |-4x + 5| - 4 ≥ - 4 

The range of 2 |-4x + 5| - 4 may also be written in interval form as follows 

[-4 , ∞)The domain of f above is the set of all values of x in the interval ( -3 , +∞) 
example