# Trabajo

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• Publicado : 8 de marzo de 2010

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PRACTICE EXERCISES FOR THE FIRST PARTIAL

NOTE: ANSWERS CAN BE FOUND AT THE END OF THIS DOCUMENT

INVERSE FUNCTIONS

Find the inverse function of[pic]; graph them together in the same set ofaxes. State the domain and range of the function and its inverse.
1. [pic]
2. [pic]
3. [pic]

Use the inverse property to show that [pic] and [pic]
4. [pic]
5. [pic]
6. [pic]

EXPONENTIALFUNCTIONS

Make a sketch of the graph of each exponential function, showing the notable points and asymptote. State the domain, range and equation of the asymptote.

7. [pic]
8. [pic]
9. [pic]LOGARITHMIC FUNCTIONS

Make a sketch of the graph of each logarithmic function, showing the notable points and asymptote. State the domain, range and equation of the asymptote.

10. [pic]
11.[pic]
12. [pic]

APPLICATION PROBLEMS – EXPONENTIAL FUNCTIONS

Population Growth
13. The population of a certain species of high school students is limited by the type of classroom required forstudying (or being senselessly tortured by math teachers) because of limited air conditioning. Under such conditions the population follows a logistic growth model [pic] where t is the time in hours. (a)Find the initial student population, (b) Find the population after 5 hours, (c) Estimate what size the population approaches after many hours have passed.

Compound Interest
14. A sum of \$1000 isinvested at an interest rate of 12% per year. Find the amounts in the account after 3 years if interest is compounded annually, semiannually, quarterly, monthly, weekly, daily and continuously.ANSWERS
1. [pic]
[pic]
Suggested values of x to substitute in f(x): -2,-1,0,1,2. Invert the columns to get coordinates for f-1(x), graph both function and inverse. You can check with Geogebra orGraphmatica.

2. [pic]
[pic]
Suggested values of x to substitute in f(x): 4,5,8,13,20. Invert the columns to get coordinates for f-1(x), graph both function and inverse. You can check with Geogebra...