Two Function Problems

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January 22nd 2008, 05:49 AM
Amy

Two Function Problems

1. The cost of sending an overnight package from New York to Atlanta is $9.80 for a package weighing up to but not including 1 pound and $2.50 for each additional pound or portion of a pound. Use the greatest integer function to create a model for the cost C of overnight of a package weighing x pounds, where x > 0. Sketch the graph of the function.

2. Your wage is $8.00 per hour plus $0.75 for each unit produced hour. So, your hourly wage y in terms of the number of units produced x is y = 8 + 0.75x.

Find the inverse function. What does each variable in the inverse function represents?

for the first one, is it
C= 9,whenx<1
=9+[2.5x],whenx>or=1

Second one,
x=(y-8)/.75
January 22nd 2008, 06:01 AM
colby2152

Quote:

Originally Posted by Amy

1. The cost of sending an overnight package from New York to Atlanta is $9.80 for a package weighing up to but not including 1 pound and $2.50 for each additional pound or portion of a pound. Use the greatest integer function to create a model for the cost C of overnight of a package weighing x pounds, where x > 0. Sketch the graph of the function.

2. Your wage is $8.00 per hour plus $0.75 for each unit produced hour. So, your hourly wage y in terms of the number of units produced x is y = 8 + 0.75x.

Find the inverse function. What does each variable in the inverse function represents?

for the first one, is it
C= 9,whenx<1
=9+[2.5x],whenx>or=1

Second one,
x=(y-8)/.75

Your second inverse function is correct, but the first function should look like this:

$C = 9.8, x < 1$
$C= 9.8+2.5(x-1), x \ge 1$
January 22nd 2008, 06:32 AM
Amy

Quote:

Originally Posted by colby2152

Your second inverse function is correct, but the first function should look like this:

$C = 9.8, x < 1$
$C= 9.8+2.5(x-1), x \ge 1$

I didn't get the second one yet.
I understood the x-1 part.
If it is $C = 9.8, x < 1$
$C= 9.8+2.5(x-1), x \ge 1$ , then what is the difference between the normal function and the greatest integer function.

Note: by normal function I meant the actual values given
January 22nd 2008, 12:13 PM
Amy

And what about the graph?

Is it a straight line parallel to x axis IN THE INTERVAL (0,1) along the x axis and from x=1 onwards straight line corresponding to y= 9.8+(x-1)2.5?
Am I right?
January 22nd 2008, 12:17 PM
colby2152

Quote:

Originally Posted by Amy

And what about the graph?

Is it a straight line parallel to x axis IN THE INTERVAL (0,1) along the x axis and from x=1 onwards straight line corresponding to y= 9.8+(x-1)2.5?
Am I right?

Your intuition is correct. It is a straight flat line (slope of zero) from zero to one. From one onwards, the line "ramps" up at an angle (slope of 2.5).