Answer:
[tex]f(x) = \left \{ {{39.99; 0 \le x \le 450} \atop {0.45x - 162.51; \ x>450}} \right.[/tex]
Step-by-step explanation:
Given
Charges: $39.99 for first 450 minutes
Charges: $0.45 for additional minutes
(a): What is x
x represents the total minutes
(b): What is f(x)
f(x) represents the total monthly cellular charges
(c): The piecewise function
For the first 450 minutes, the function is:
[tex]f(x) = 39.99;\ 0 \le x \le 450[/tex]
For additional minutes.
In (a), the total minutes is x.
So, we have:
Total Charges = Charges for first 450 minutes + Charges for additional minutes * (Minutes after 450 minutes)
[tex]Total\ Charges = 39.99 + 0.45 * (x - 450)[/tex]
[tex]f(x) = 39.99 + 0.45 * (x - 450)[/tex]
Open bracket
[tex]f(x) = 39.99 + 0.45x - 0.45 * 450[/tex]
[tex]f(x) = 39.99 + 0.45x - 202.5[/tex]
Collect Like Terms
[tex]f(x) = 0.45x+39.99 - 202.5[/tex]
[tex]f(x) = 0.45x-162.51[/tex]
The range of the above function is: x > 450.
So, the piecewise function is:
[tex]f(x) = \left \{ {{39.99; 0 \le x \le 450} \atop {0.45x - 162.51; \ x>450}} \right.[/tex]
