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How do you write #f(x)= |7/6x+4/3|# as a piecewise function?

Answer 1

Julia Adams

See below.

The definition of absolute value.

#|a|=acolor(white)(8888888)# If and only if #color(white)(8888888)a>=0#

#|a|=-acolor(white)(8888)# If and only if #color(white)(8888888)a<0#

First we recognise that if #7/6x+4/3<0# , we have #-(7/6x+4/3)#

And if #7/6x+4/3>=0color(white)(88)# we have #color(white)(888)(7/6x+4/3)#

#7/6x+4/3<0=>x<-8/7#

#7/6x+4/3>=0=>x<-8/7#

So piecewise we have:

#f(x)=[(-7/6x-4/3 , ->x<-8/7),(,),(7/6x+4/3,->x>=-8/7)]#

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Answer 2

Savannah Anderson

The piecewise function for ( f(x) = \left| \frac{7}{6}x + \frac{4}{3} \right| ) would be:

[ f(x) = \begin{cases} \frac{7}{6}x + \frac{4}{3} & \text{if } x \geq -\frac{4}{7} \ -\left( \frac{7}{6}x + \frac{4}{3} \right) & \text{if } x < -\frac{4}{7} \end{cases} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.