Question

a certain model of cell phone sells for $999. each year, the value of the phone increases by 6%. what are the domain and range of a function that represents this scenario?

the domain is $-infty < x < infty$, and the range is $y geq 999$.

the domain is $x geq 0$, and the range is $0 < y leq 999$

the domain is $x geq 0$, and the range is $y geq 999$

the domain is $-infty < x < infty$, and the range is $0 < y leq 999$

Explanation:

Step1: Analyze the domain

The scenario is about the value of a cell phone over time. Time (represented by \( x \), the number of years) cannot be negative, so \( x \geq 0 \). This eliminates options with domain \( -\infty < x < \infty \).

Step2: Analyze the range

The initial value of the phone is $999, and each year its value increases by 6%. So the value LXI0 of the phone will always be at least $999 (since it's increasing from 999) and will keep increasing. So the range should be \( y \geq 999 \).

Answer:

The domain is \( x \geq 0 \), and the range is \( y \geq 999 \) (the third option among the given choices, assuming the third option is phrased as "The domain is \( x \geq 0 \), and the range is \( y \geq 999 \)").