Question

The function $c\left(x\right)\ =\ 0.5x+70\ $ represents the cost $c$ (in dollars) of renting a truck from a moving company, where $x$ is the number of miles you drive the truck.

Answer 1

Answer:

Step-by-step explanation:

A line is defined by the expression

f (x) = m * x + b      or      y = m * x + b

where me is the slope of the line and b is the y-intercept.

In this case, the value of the slope m is 0.5, which expressed as a fraction is 1/2, and the value of y-intercept is 70.

So, to graph the line, you must first plot the y-intercept at 70. Then you must plot a second point, considering that:

m=Δy÷Δx  so $m=\frac{1}{2}$

In other words, for every 2 units that you move to the right, you must move 1 unit up.

In this way you get the graphic of the attached image.

The domain of a function is the set of values ​​that the independent variable x can take. In this case x represents the number of miles the truck drives, the value of which cannot be negative. Then the values ​​of x must be equal to or greater than zero. Then, the domain of the line in this case, expressed as an inequality, is 0≤x≤∞

In the graph you can see that the cost c (in dollars) of renting a truck from a moving company when the number of miles the truck drives is zero has a value of $ 70. In this way you can determine that the cost of x number of miles is equal to or greater than 70. Then the image of the function, expressed as an inequality, is 70≤y≤∞