The function c(x) = 0.5x+70 represents the cost c (in dollars) of renting a truck from a moving company, where x is the number o

Answer:

b) h(x) = –2x + 200

Step-by-step explanation:

The moving rates from one company can be characterized by the function f(x) = 3x + 400, where x indicates the miles moved.

Another moving company's rates can be defined as g(x) = 5x + 200.

To find the function that represents the difference in costs between the two moving companies, we express it as h(x) = f(x) – g(x).

Thus, we get:

h(x) = 2x + 200

h(x) = –2x + 200

h(x) = 5x – 200

h(x) = 5x + 600

Function given: c(x) = 0.5x + 70.

Here, c represents the cost in dollars while x indicates the miles driven in the truck.

By comparing this with the slope-intercept format y=mx+b, we find:

Slope m = 0.5, which can be expressed as 1/2.

The y-intercept b = 70.

To graph this, we start by plotting the y-intercept at 70 and then add more points based on the rise/run ratio, which is 1/2.

The plotted line shown in red illustrates the function.

It can be observed that the initial cost is $70, corresponding to zero miles driven.

The x values denote the domain while C(x) portrays the range.

We can use x values that are 0 or above, and C values that are 70 or more.

Thus, Domain: x≥0 and Range: C(x)≥70.