Ireally am struggling with algebra 2

Step-by-step explanation:

So to solve this we have to consider the piecewise definition of an absolute value function.

|x| =

f(x) = -x if x<0

and

f(x) = x if x ≥ 0

Lets explain this a bit:

At 0 for the absolute value function there is a breaking point. This "breaking point" occurs because we are going between negative and positive values. Meaning that before 0 we have negative numbers and after 0 we have positive numbers. However, we know that absolute value bars mean that the value inside cannot be negative to we have to redefine the function to fit what we want. That is why when x<0 we define our function as -x because whatever negative value we get when x<0 will be multiplied by that negative and then become positive!

So for this question you apply the same "breaking point" thinking.

So we can say that |4x-1| is equal to

f(x) = -(4x-1) when 4x-1<0

and

f(x) = 4x-1 when 4x-1 ≥ 0

We can also solve this inequalities for our breaking point values (where 4x-1 = 0)

So 4x - 1 = 0

4x = 1

x = 1/4

So we could say:

f(x) = -(4x-1) when x < 1/4

and

f(x) = 4x-1 when x ≥ 1/4

Hopefully this makes sense!

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