QuestionDefine the absolute value function $f(x)=|4x+7|$ as a piecewise function.

Studdy Solution
Now we can write the absolute value function $f(x)=|4x+7|$ as a piecewise function with the simplified conditions.
$$f(x) = \left\{\begin{array}{ll} -(4x+7), & x<-\frac{7}{4} \\ 4x+7, & x \geq -\frac{7}{4} \end{array}\right.$$
So, the absolute value function $f(x)=|4x+7|$ can be written as a piecewise-defined function with linear parts as follows$$f(x) = \left\{\begin{array}{ll} -(4x+7), & x<-\frac{7}{4} \\ 4x+7, & x \geq -\frac{7}{4} \end{array}\right.$$