Question

the graph represents the data cost for monthly internet service for a cell phone. which function, c(x), represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month? cell phone internet service monthly cost ($) 60 55 50 45 40 35 30 25 20 15 10 5 0 1 2 3 4 5 6 7 8 9 10 11 12 gigabytes used c(x) = {15, 0 <= x <= 2; 5x + 10, 2 < x <= 6; 50, 6 < x} c(x) = {15, 0 <= x < 2; 5x + 20, 2 <= x < 6; 50, 6 <= x} c(x) = {15x, 0 <= x <= 2; 20x + 5, 2 < x <= 6; 50x, 6 < x} c(x) = {15x, 0 <= x < 2; 5x + 10, 2 <= x < 6; 50x, 6 <= x}

Explanation:

Step1: Analyze $0\leq x\leq2$

From the graph, when $0\leq x\leq2$, the monthly cost $C(x) = 15$.

Step2: Analyze $2 < x\leq6$

The line - segment for $2 < x\leq6$ passes through the points $(2, 20)$ and $(6, 40)$. The slope $m=\frac{40 - 20}{6 - 2}=\frac{20}{4}=5$. Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,20)$: $y-20 = 5(x - 2)$, which simplifies to $y=5x+10$. So for $2 < x\leq6$, $C(x)=5x + 10$.

Step3: Analyze $x>6$

From the graph, when $x>6$, the monthly cost $C(x)=50$.

Answer:

$C(x)=

$$\begin{cases}15, &0\leq x\leq2\\5x + 10, &2 < x\leq6\\50, &6 < x\end{cases}$$

$