Question 114024
Please help. Thank you very much
Write a piecewise function for f(x)=|24x-3| 

<pre>
When 24x-3 is non-negative, the following are true

1.   f(x) = |24x-3| = +(24x-3) = 24x-3

2.    24x-3 <u>></u> 0
        24x <u>></u> 3
          x <u>></u> {{{3/24}}}
          x <u>></u> {{{1/8}}} 

Therefore f(x) = 24x-3 when x <u>></u> {{{1/8}}}

When 24x-3 is negative, the following are true

1.   f(x) = |24x-3| = -(24x-3) = -24x+3

2.    24x-3 < 0
        24x < 3
          x < {{{3/24}}}
          x < {{{1/8}}} 

Therefore f(x) = -24x+3 when x < {{{1/8}}}

Now we put those together:

f(x) =  24x-3 when x <u>></u> {{{1/8}}}
f(x) = -24x+3 when x < {{{1/8}}}

We normally write this as:

       <font face = "symbol">ì</font> 24x-3 when x <u>></u> 1/8
f(x) = <font face = "symbol">í</font>
       <font face = "symbol">î</font>-24x+3 when x < 1/8

The graph of f(x) looks like this:

{{{graph(200,50,-1.3,1.3,-1.3,1.3,abs(24x-3))}}}

Edwin</pre>