pre-calculus honors

Generate a function that models the situation. Consider the type of function described—it is not linear!
A shipping company charges \$4 for the first pound and \$3 for each additional pound or part thereof.
As you try to come up with the equation, consider the following:
-How much should you be charged if your shipment weighs 0.7 pounds? \$4
-How much should you be charged if your shipment weighs 1.0 pounds? \$4
-How much should you be charged if your shipment weighs 1.3 pounds? \$7
-How much should you be charged if your shipment weighs 1.8 pounds? \$7
-How much should you be charged if your shipment weighs 2.0 pounds? \$7
-How much should you be charged if your shipment weighs 2.1 pounds? \$10
Make sure that your function gives the correct answer for each of these.
Can someone pease help, all I could figure out was that it uses linear programming and that its a step-wise function. Thanks :)

1. 👍 0
2. 👎 0
3. 👁 144
1. It is indeed a step function, with each step lasting one pound. Note that the beginning of the step is included in the interval, for example, 2 pounds to 2.9999999 pounds will cost 7\$. The end of the step must be excluded to avoid two costs for the same weight. This is also one of the properties of a function.

This property can be verified by the vertical line rule, which says that any vertical line drawn on the domain of the function cannot intersect the function at more than once.

For an illustration of the function, see:
http://img402.imageshack.us/img402/5807/1261088031.png

1. 👍 0
2. 👎 0
2. yes but what is the function?

1. 👍 0
2. 👎 0
3. What is the y= function? That's what i don't know.

1. 👍 0
2. 👎 0
4. "Generate a function..." means it is one that the student is to make it up. It doesn't usually have a name because it is a custom-made function to suit the question, although you could name it anything you want.
The "y" function is the numbers in the y-axis, namely cost of shipping in dollars.

The function has been shown in the graph. Study the graph to make sure you understand how it is made up.
Then try to formulate a mathematical expression for the function. You may have to use an existing function to help you put the function in mathematical terms. The existing function is called floor(x).
Floor(x) is a function defined as the largest integer not exceeding x.

For example,
floor(4)=4
floor(4.2)=4
floor(4.999)=4
and
floor(5)=5

Using this function and some doing some figuring, you should be able to come up with a mathematical function that looks like what is shown in the graph in the link.

1. 👍 0
2. 👎 0
5. Thanks I figured it out :)

1. 👍 0
2. 👎 0
6. f(x)=4+3*[[x]]

1. 👍 0
2. 👎 0
7. You're almost there. The only problem is that it does not work for integer number of pounds, for example, for weight = 1 pound, the cost is 7 dollars according to your function.

The problem is due to an error on my part. Each step on the graph in the earlier link should have had the interval inclusive on the right, and exclusive on the left, since the price goes up only after the weight exceeds an integer number of pounds.

http://img696.imageshack.us/img696/8564/1261088031a.png

Consequently the function that should have been used is the ceiling function, which is defined as :

ceiling(x) = smallest integer that is greater than or equal to x.

The required shipping cost function should therefore be
f(x) = 1 + ceiling(x)
where x is the number of pounds.

Check my thinking.

1. 👍 0
2. 👎 0

Similar Questions

1. pre-calculus honors

GENERATE A FUNCTION THAT MODELS THE SITUATION. Consider the type of function described—it is not linear! A shipping company charges \$4 for the first pound and \$3 for each additional pound or part thereof. As you try to come up

asked by annemarie on December 17, 2009
2. pre-calculus honors

GENERATE A FUNCTION THAT MODELS THE SITUATION. Consider the type of function described—it is not linear! A shipping company charges \$4 for the first pound and \$3 for each additional pound or part thereof. As you try to come up

asked by annemarie on December 17, 2009
3. algebra

1. Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern. Do not state which situation is linear and which is nonlinear. Your classmates will need to determine which is

asked by ssuban on November 10, 2016
4. algebra

Describe a situation that models a linear pattern and then describe a situation that models a nonlinear pattern. Do not state which situation is linear and which is nonlinear. Your classmates will need to determine which is which

asked by Mary on October 26, 2018
5. Algebra

HOURS STUDYING AVG GRADE 0 62 1 78 2 85 5 74 WHICH TYPE OF FUNCTION IS MOST LIKELY TO MODEL THESE DATA? A. LINEAR FUNCTION W/POSITIVE SLOPE B. LINEAR FUNCTION W/NEGATIVE SLOPE C. NON-LINEAR THAT DECREASE THE INCREASE D. NON LINEAR

asked by Blake on April 6, 2016
6. math

A tire company determines that to manufacture a certain type of tire, it costs \$9000 to set up the production process. Each tire that is produced costs \$21 in material and labor. The company sells this tire to wholesale

asked by Marie P. on August 4, 2014
7. Algebra

HOURS STUDYING----- AVG GRADE 0-------------------- 62 1-------------------- 78 2-------------------- 85 5-------------------- 74 WHICH TYPE OF FUNCTION IS MOST LIKELY TO MODEL THESE DATA? A. LINEAR FUNCTION W/POSITIVE SLOPE B.

asked by Kimmy on April 7, 2016
8. Calculus HELP ASAP

Listed below are four types of functions. Which does not possess a derivative of the same type? a) exponential function b) logarithmic function c) sinusoidal function d) linear function e) NO RESPONSE

asked by Anonymous on January 23, 2019
9. Math

Determine whether each verbal description represents a linear function or not. Correct me if I'm wrong on any of these!! 1. Jova walks quickly for 25 minutes then she rests for 5 minutes before continuing on for another 10

asked by Leah on October 30, 2013
10. Math

Determine whether each verbal description represents a linear function or not. Correct me if I'm wrong on any of these!! 1. Jova walks quickly for 25 minutes then she rests for 5 minutes before continuing on for another 10

asked by Emily on October 30, 2013

More Similar Questions