The 15% discount for home gym, and the $889 cost of the Flex 3,000 gives;
1. f(x) = 0.85•x + 139.95
2.
- With the deal, Charlotte's before tax cost is $895.6
- The deal cost is more than the initial price making the deal not worth it.
3. The domain is; 889 < x < ∞
The range is; 895.6 ≤ f(x) ‹ ∞
<h3>How can the function notation for the cost be found?</h3>
1. The percentage discount Charlotte gets = 15% = 0.15
Cost of the 6 months subscription = $139.95
f(x) = Final before tax
x = Price of the home gym equipment
Therefore;
Given the 15% off, we get;
f(x) = (1-0.15)•x + 139.95
Which gives;
2. Question 1
Cost of the Flex3000, <em>x</em> = $889
Therefore;
f(889) = 0.85 × 889 + 139.95 = 895.6
Charlotte's before–tax cost with the deal is therefore, $895.6
Given that the workout channel holds no value to Charlotte, and the deal cost is higher than the initial cost, it isn't worth it for her to pay for the subscription to get the 15% discount
3. The domain if the Awesome Flex is the cheapest option, is the possible initial price of the home gym equipment.
The domain is therefore;
The range is the possible values of the before tax cost.
The range is therefore;
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![\left[\begin{array}{ccc}\boxed{\boxed{ 4/6 = 6/9}}\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cboxed%7B%5Cboxed%7B%204%2F6%20%3D%206%2F9%7D%7D%5Cend%7Barray%7D%5Cright%5D%20)
This would be because 4/6 is almost 1 as a whole, and also, 6/9 is almost 1, as a whole, so this would totally make sense for this to be a proportional.