The best description of the function that represents the situation is:
**It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.**
Here’s why:
- Multiplying the price on the tag by 75% (or 0.75) means the final cost is directly proportional to the original price.
- A function of the form \( f(x) = 0.75x \) is a linear function because it has the form \( f(x) = mx + b \) where \( m = 0.75 \) and \( b = 0 \). Therefore, it is a linear function.
- In a linear function, the ratio of the change in the final cost (output) to the change in the price tag (input) is constant, which is true here since the ratio is always 0.75.
The final cost of a sale item is determined by multiplying the price on the tag by 75%. Which best describes the function that represents the situation?
It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant.
It is linear because the function is continuous.
It is nonlinear because the final cost is determined by multiplying each price tag by 0.75.
It is nonlinear because the price tag and final cost columns do not have the same common difference.
1 answer
1 answer