Critical Thinking Look back at Section 4.3, wherethe basic properties of graphs of

In Exercises 16, list the transformations needed to trans- form the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 16, list the transformations needed to trans- form the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 16, list the transformations needed to trans- form the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 16, list the transformations needed to trans- form the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 16, list the transformations needed to trans- form the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 16, list the transformations needed to trans- form the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 713, list the transformations needed to transform the graph of into the graph of the given function. (Section 3.4 may be helpful.)

In Exercises 1419, sketch a complete graph of the function.

In Exercises 1419, sketch a complete graph of the function.f 1x2 a 5 2b

In Exercises 1419, sketch a complete graph of the function.

In Exercises 1419, sketch a complete graph of the function.

In Exercises 1419, sketch a complete graph of the function.

In Exercises 1419, sketch a complete graph of the function.

In Exercises 2021, match the functions to the graphs. Assume and a 7 1 c 7 1. h1x2 ax5 g1x2 ax 3 f 1x2 ax

In Exercises 2021, match the functions to the graphs. Assume and a 7 1 c 7 1.. k1x2 3cx 2 h1x2 cx5 g1x2 3cx f 1x2 cx

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.f 1x2 e x2

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.h1x2 ex ex 2 f 1x2 ex ex

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.k1x2 2 ex e g x 1x2 2x x

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.

In Exercises 2229, find a viewing window (or win- dows) that shows a complete graph of the function.g1x2 10 1 9ex 2

In Exercises 3034, determine whether the function is even, odd, or neither. (See Excursion 3.4A.)

In Exercises 3034, determine whether the function is even, odd, or neither. (See Excursion 3.4A.)

In Exercises 3034, determine whether the function is even, odd, or neither. (See Excursion 3.4A.)

In Exercises 3034, determine whether the function is even, odd, or neither. (See Excursion 3.4A.)f 1x2 ex ex

In Exercises 3034, determine whether the function is even, odd, or neither. (See Excursion 3.4A.)f 1x2 ex2

Use the Big-Little concept (see Section 4.4) to explain why is approximately equal to when x is large.

In Exercises 3639, find the average rate of change of the function. (See Section 3.7).. as x goes from 1 to 3

In Exercises 3639, find the average rate of change of the function. (See Section 3.7).

In Exercises 3639, find the average rate of change of the function. (See Section 3.7).

In Exercises 3639, find the average rate of change of the function. (See Section 3.7).

In Exercises 4043, find the difference quotient of the function. (See Section 3.7.)

In Exercises 4043, find the difference quotient of the function. (See Section 3.7.)g1x2 5x2

In Exercises 4043, find the difference quotient of the function. (See Section 3.7.)

In Exercises 4043, find the difference quotient of the function. (See Section 3.7.)f 1x2 ex e x f 1x2 2x 2x

In Exercises 4449, list all asymptotes of the graph of the function and the approximate coordinates of each local extremum. (See Section 4.3.)

In Exercises 4449, list all asymptotes of the graph of the function and the approximate coordinates of each local extremum. (See Section 4.3.)

In Exercises 4449, list all asymptotes of the graph of the function and the approximate coordinates of each local extremum. (See Section 4.3.)

In Exercises 4449, list all asymptotes of the graph of the function and the approximate coordinates of each local extremum. (See Section 4.3.)

In Exercises 4449, list all asymptotes of the graph of the function and the approximate coordinates of each local extremum. (See Section 4.3.)

In Exercises 4449, list all asymptotes of the graph of the function and the approximate coordinates of each local extremum. (See Section 4.3.)

If you deposit at interest, compounded annually and paid from the day of deposit to the day of withdrawal, your balance at time t is given by How much will you have after 2 years? after 3 years and 9 months?

The population of a colony of fruit flies t days from now is given by the function a. What will the population be in 15 days? in 25 days? b. When will the population reach 2500?

A certain type of bacteria grows according to the function where the time x is measured in hours. a. What will the population be in 8 hours? b. When will the population reach 1 million?

According to data from the National Center for Health Statistics, the life expectancy at birth for a person born in year x is approximated by the function below. a. What is the life expectancy of someone born in 1980? in 2000? b. In what year was life expectancy at birth 60 years?

The number of subscribers, in millions, to basic cable TV can be approximated by the function where corresponds to 1970. (Source: The Cable TV Financial Datebook and The Pay TV Newsletter) a. Estimate the number of subscribers in 1995 and in 2005. b. When does the number of subscribers reach 70 million? c. According to this model, will the number of subscribers ever reach 90 million?

The estimated number of units that will be sold by a certain company t months from now is given by a. What are the current sales What will sales be in 2 months? in 6 months? From examining the graph, do you think that sales will ever start to increase again? Explain.

a. The function gives the percentage of the population (expressed as a decimal) that has seen a new TV show t weeks after it goes on the air. What percentage of people have seen the show after 24 weeks? b. Approximately when will of the people have seen it?

a. The beaver population near a certain lake in year t is approximated by the function What is the population now and what will it be in 5 years? b. Approximately when will there be 1000 beavers?

Critical Thinking Look back at Section 4.3, where the basic properties of graphs of polynomial functions were discussed. Then review the basic properties of the graph of discussed in this section. Using these various properties, give an argument to show that for any fixed positive number a, where it is not possible to find a polynomial function such that for all numbers x. In other words, no exponential function is a polynomial function.

Critical Thinking For each positive integer n, let be the polynomial function below. a. Using the viewing window with and graph and on the same screen. Do the graphs appear to coincide? b. Replace the graph of by that of , then by , and so on until you find a polynomial whose graph appears to coincide with the graph of in this viewing window. Use the trace feature to move from graph to graph at the same value of x to see how accurate this approximation is. c. Change the viewing window so that and Is the polynomial you found in part b a good approximation for in this viewing window? If not, what polynomial is a good approximation?