Chapter ISG, Problem 3.6.3P

To determine

To calculate the range and domain

Answer to Problem 3.6.3P

(Write the final answer here)

Explanation of Solution

Given information:

The necklace is 8cm when Kate starts.

Each bead adds 2mm.

Maximum length of necklace is 60cm.

Formula used:

Function formation and solvation.

Calculation:

Converting 20mm into cm,

  $10mm=0.2cm$

Hence the function for the additional length of necklace,

  $f(x)=8+0.2x$

Where, x is the number of beads

The maximum length is 60, therefore, substituting the values in function,

  $60=8+0.2x$

Shifting right hand-side values to left-hand side,

  $0.2x=60-8$

So,

  $0.2x=52$

Cross-multiplying,

  $x=\frac{52}{0.2}$

On solving,

  $x=260$

Hence, the range is

  $range=\{y:8\le y\le 60\}$

And domain is,

  $domain=\{x:1\le x\le 260\}$