Question

The function c(x) = 0.5x+70

Answer 1

Given:

The cost function

$c(x) = 0.5x + 70$

where x is the number of miles the truck has been driven.

Graph:

We must first construct the table. We start by manually calculating the valueof c(x) for every x starting with x = 0.

We may take any real values of x ≥ 0 to make our table. Here, I have chosen x = 0, 10, 20, 30, 40, 50, 60, 70.

We then plot the points of x on the x-axis and of c(x) on the y (or vertical) axis.

The graph as well as the table have been uploaded as images.

Concept & Explanation:

Domain - the domain of the given function is the set of all the values that x can take for the function to be valid.

Range - the range of the given function is the set of all the values c(x) will take for each value of x in the domain.

Here, x represents the number of miles driven and c(x) represents the cost of renting. Clearly, neither x nor c(x) can be negative. Moreover, both these values will be real numbers.

Note that x may be zero (if the renter doesn't drive the truck at all) or x may be positive.

Taking the case when x = 0,

$c(x)=0.5(0) +70 = 70$

Therefore, we have identified the lower limits of both the domain and the range.

Seeing as the moving company has not imposed an upper limit on the number of miles that can be written, we can not reasonable identify any upper bounds for the domain and range.

So, domain is the set 0 ≤ x < ∞

And, range is the set 70 ≤ c(x) < ∞