Question

Charlotte has been saving up to buy a home gym so she can work out at home without having to pay for a
gym membership or worry about travel when the weather is bad (she lives in Minnesota where it snows
frequently). One day, she sees an ad for a 15% off sale at a fitness equipment store and decides it's a great
time to buy the home gym! She notices the fine print says that to get the 15% off the home gym, she has to
pay $139.95 up front for a 6-month subscription to a workout channel, which holds no value to her.
1. Using function notation, write an expression for the final before-tax cost, f(x), of the purchase
based on the initial price, x, of the home gym equipment with this deal.
2. She was considering purchasing the Awesome Flex3000 for $889. Using your function from
question 1, what would Charlotte be Charlotte's before-tax cost with the deal? Is it worth it for
her to pay for the subscription to get 15% off? Explain your answer.
3. What is the domain and range of f(x) if the Awesome Flex is the cheapest option at the store?

Answer 1

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.

1. With the deal, Charlotte's before tax cost is $895.6
2. 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) ‹ ∞

How can the function notation for the cost be found?

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;

• f(x) = 0.85•x + 139.95

2. Question 1

Cost of the Flex3000, x = $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;

• 889 < x < ∞

The range is the possible values of the before tax cost.

The range is therefore;

• 895.6 ≤ f(x) ‹ ∞

Learn more about writing equations here:

https://brainly.com/question/11331093

#SPJ1