Question

A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour
(A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours
(B) Graph F(x) for 0 < x s 15
(C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Answer 1

Answer and Step-by-step explanation:

Given:

Charges includes 10 hour per month = $50

Charges for additional hour = $9

Piecewise definition of cost F(x) for a month in which a member use a car for  hours.

Find limits?

Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist.

Lim x → 10- F(x) = 50$

Lim x → 10 [ 9x – 70] = 9( 10) – 70  

                                = 90 – 70

                                = 20 > 10

Limit does not exist.

Lim x → 10+ F(x) = 50$

Lim x → 10+  F(x) = Lim x → 10+   [90x – 70]

                         = 90 – 70

                          = 20 > 10

Limit does not exist.

Lim x → 10 F(x) = 50$

An integer or an decimal.

The limit does not exist.

Answer 2

The piece wise definition of the cost $f(x)$ for a month in which a member uses a car for $x$ hours is given by the equation,$f(x)= 50+9(x-10)$.

Given,

Membership plan is $\ 50$ per month.

We have to write a piece wise definition of the cost $f(x)$ for a month in which a member uses a car for $x$ hours.

Here, $50$ per month fees includes 10 hours of driving each month, so the cost for a month is given as,

$f(x)= 50+9(x-10)$

Here $x$ is the no. of additional hours for the month.

Further,

$f(x)= 9x-40$.

Now at,

$lim _{x \to 10^+}f(x) = 9\times 10-40$

Or,

$f(x)= 90-40\\f(x)=50$

Similarly, at left limit,

$lim _{x \to 10^-}f(x) = 9\times (-10)-40$

Or,

$f(x)=-90-40$

$f(x)=-130$

Finally at $x=10$, $f(x)=9\times10-40$

$f(x)=90-40\\f(x)=50$

Since $lim{x \to}10^+$ $\neq limx\to 10^-\neq f(x) (at x= 10)$

So the required function $f(x)$ is discontinuous at $x=10$

Hence the piece wise definition of the cost $f(x)$ for a month in which a member uses a car for $x$ hours is given by the equation,$f(x)= 50+9(x-10)$.

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