Question

Which functions C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month

Answer 1

Answer:

The answer in the procedure

Step-by-step explanation:

Let

x ----> the number of gigabytes used in a month

C(x)------> the monthly cost in dollars

step 1

For the interval ----> [0,2]

$0\leq x\leq 2$

$C(x)=15$

step 2

For the interval ---->(2,6]

$2< x\leq 6$

Find the equation of the line

Find the slope

we have

$(2,20),(6,40)$

$m=(40-20)/(6-2)=5$

The equation of the line in to point slope form is equal to

$y-20=5(x-2)\\ y=5x-10+20\\ y=5x+10$

therefore

$C(x)=5x+10$

step 3

For the interval ----> (6,∞]

$x> 6$

$C(x)=50$

Answer 2

Answer:

C(x)=$15, 0\leq x\leq 2$

        $5x+10, 2<x\leq 6$

          $50,$ 6<x≤∞

Step-by-step explanation:

C(x) represents the monthly cost in dollars in terms of x, the number of gigabytes used in a month

Lets find C(x) on each interval (for every line graph)

first interval 0 to 2

the value of y is 15 on the interval 0 to 2

Its horizontal line . So equation is c(x)=the constant y value

$C(x)= 15, 0\leq x\leq 2$

Second interval 2 to 6

Pick two points to get the equation of that line

(3,25) and (6,40)

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{40-25}{6-3} =5$

Equation of the line is using m=5 and (3,25)

$y-y1=m(x-x1)$

$y-25=5(x-3)$

$y-25=5x-15$

$y=5x+10$

$C(x)= 5x+10, 2<x\leq 6$

Now we look at the third interval

6 to infinity

For the third graph , the value of y is 50 (constant)

It is a horizontal line

So $C(x)= 50,$ 6<x≤∞

We got three equations for C(x)

C(x) is a piecewise function

C(x)=$15, 0\leq x\leq 2$

        $5x+10, 2<x\leq 6$

          $50,$ 6<x≤∞