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

Which functions C(x) represents the monthly cost in dollars in terms of x, the number-example-1

2 Answers

3 votes

Answer:

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

User KMLong
by
8.4k points
1 vote

Answer:

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≤∞

User Tsu
by
8.6k points

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