Math 138 Review for Final
Linear Functions:
You are about to take a trip for 7 days here are two rental offers: (i) Hertz will give you 28 cents per mile and $47 per day, and (ii) Avis will give you 27 cents per mile and $48 per day. Then sketch the cost functions for Hertz and Avis together.
Concept of Inverse Functions:
The graph of the function
is given below:
Suppose we restrict the domain of to be and if and Find and
Suppose we restrict the domain of to be sketch
Concepts of graphs of functions:
Suppose the graph of
is given below. Then
graph
graph
graph
graph
Polynomial Functions.
A company's profit function (when number of units are produced) satisfies the following conditions:
the profit function breaks even at and units
the profit function changes signs (from to or vise versa) at but does not change sign at and
Then (a) find a profit function which satisfies all the conditions mentioned above. (b) Predict if 400 units is produced, would the company be profitable?
Sketch the graph which you have found in question above
For ,
find the interval(s) where
sketch the graph for .
Rational Functions.
Find two rational functions satisfying ALL the following conditions:
has two vertical asymptotes at and respectively,
has a horizontal asymptote at
Suppose the average revenue per unit for producing
number of units for a manufacturing company is given by
If units are produced, find the average revenue per unit.
What is the maximum or minimum average revenue per unit?
Exponential and Logarithmic Functions.
Find the inverse function for the followings and graph the function and its inverse together:
(New) If find the inverse functions for and respectively.
(New) If find the inverse functions for and respectively.
(New) If find the inverse functions for and respectively.
Solve the following equations. (Must show your works)
.
The number of some bacteria present after days of a laboratory experiment is given by
When will the bacteria population reach
Graph the function
A model for the number of people in a college community who have heard a certain rumor is where is the total population of the community and is the number of days that have elapsed since the rumor began.
In a community of students, how many days will elapse before students have heard the rumor?
Plot step by step.