91Ó°ÊÓ

The function $C\left(x\right)=0.25x+35$represent the cost of renting a moving truck for a day and x is the number of miles driven.

To find the cost of renting truck for drive of 40 miles.

We have $x=40$

Substitute $x=40$in role="math" localid="1646585776759" $C\left(x\right)=0.25x+35$and solve it.

$$\begin{gathered} C\left(x\right)=0.25x+35 \\ =0.25\left(40\right)+35 \\ =45 \end{gathered}$$

The cost for 40 miles is $45.

To find how many miles did you drive, for the cost of renting the moving truck $80.

We have $C\left(x\right)=80$

Substitute $C\left(x\right)=80$in $C\left(x\right)=0.25x+35$and find x.

$$\begin{gathered} C\left(x\right)=0.25x+35 \\ 80=0.25x+35 \\ \frac{45}{0.25}=x \\ 180=x \end{gathered}$$

You can drive 180 miles

The cost should not more than $100. So, Cost is less than equal to $100.$C\left(x\right)≤100$

Find x

$$\begin{gathered} C\left(x\right)≤100 \\ 0.25x+35≤100 \\ x≤\frac{65}{0.25} \\ x≤260 \end{gathered}$$

You can travel maximum 260 miles.

Find implied domain of C.

C(x) is function of x and x is distance in miles so it can not be 0.

It can be any positive number.

So the implied domain of C is$\left\{x|xâ‰\yen 0\right\}$.

To find the slope, compare the function C(x) with standard linear equation $y=mx+b$where m is slope of the line and b is y-intercept.

The slope represent charge per mile.

In $C\left(x\right)=0.25x+35$, $m=0.25$

So slope is 0.25.

To find the y-intercept, compare the function C(x) with standard linear equation $y=mx+b$where m is slope of the line and b is y-intercept.

The y-intercept represent fixed charge per day.

In $C\left(x\right)=0.25x+35$, $b=35$

y- intercept is 35.