Question

Write the absolute value function as a​ piecewise-defined function with linear parts.

Answer 1

The piecewise-defined function with linear parts ​f(x)= |2x + 9|

f(x) = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

How to write piecewise functions?

To write this function as a piecewise function, you have to use the definition of absolute value.

The absolute value equation is; ​f(x)= |2x + 9|

The definition says that;

|x| = {x   x ≥ 0)

     {-x   x < 0}

Applying this definition to the function you get:

|2x + 9| = {2x + 9   2x + 9 ≥ 0)

     {-2x - 9   2x + 9 < 0}

After simplifying the inequalities you get:

|2x + 9| = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

So finally you can write the piecewise  function as:

f(x) = {2x + 9   x ≥ -9/2)

     {-2x - 9   x < 9/2}

Read more about piecewise function at; brainly.com/question/18499561

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