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

The answer in the procedure

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

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

`5x+10, 2<x\leq 6`

`50,` 6<x≤∞

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 = (y_2-y_1)/(x_2-x_1) =(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≤∞