Question

Clara earns at least $36.75 but not more than $98 working. She earns $12.25 per hour. The number of hours it takes Clara to earn p dollars is modeled by a function. t(p)=p12.25 What is the practical range of the function?

Answer 1

The answer is all real numbers from 3 to 8, inclusive 

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Answer 2

The range of the function modelling the number of hours it takes clara to earn p dollars is;

A set of all real numbers from 3 to 8

Minimum dollars she earns working; p_min = $36.75

Maximum dollars she earns working; p_max = $98

number of hours it takes her to earn p dollars is given by;

t(p) = p/12.25

Now, range of a function is a set of all possible output values.

Thus, t(36.75) = 36.75/12.25

t(36.75) = 3 hours

Similarly;

t(98) = 98/12.25

t(98) = 8 hours

Since minimum time is now 3 hours and maximum time is now 8 hours, then the range of the function is;

3 ≤ t ≤ 8 which is a set of all real numbers from 3 to 8

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