Exam 4: Inverse, Exponential, and Logarithmic Functions

Write the word or phrase that best completes each statement or answers the question. - $\text { Explain why } \log _ { 2 } 13 \text { is between } 3 \text { and } 4 \text {. }$

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = \frac { 4 } { x + 6 } , \quad g ( x ) = \frac { 6 x + 4 } { x }$

Use a graphing calculator to graph the function using the given viewing window. Use the graph to decide if the function is one-to-one. If the function is one-to-one, give the equation of the inverse function. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - x + 3 ; [ - 2,4 ] \text { by } [ - 20,20 ]$

Match the function with its graph. - $f ( x ) = \log _ { 3 } x$

Write an equation for the graph given. The graph represents an exponential function f with base 2 or 3, translated and/or reflected. -

Decide whether or not the functions are inverses of each other.Use the definition of inverses to determine whether f and g are inverses. - $f ( x ) = 4 x - 3 , \quad g ( x ) = \frac { x + 4 } { 3 }$

Write the word or phrase that best completes each statement or answers the question. -In the formula $\mathrm { N } = \mathrm { Ie } \mathrm { kt } , \mathrm { N }$ is the number of items in terms of an initial population I at a given time $\mathrm { t }$ and $\mathrm { k }$ is a growth constant equal to the percent of growth per unit time. There are currently 68 million cars in a certain country, increasing by $1.2 \%$ annually. How many years will it take for this country to have 77 million cars? Round to the nearest year.

Write in logarithmic form. - $322 / 5 = 4$

Graph the function. Give the domain and range. - $f(x)=\log _{5}(x-2)$

For the function as defined that is one-to-one, graph f and f-1 on the same axes. - $f(x)=\sqrt{x+6}$

Write the word or phrase that best completes each statement or answers the question. - $\text { Without using a calculator, explain why } 2 \pi \text { must be greater than } 8 \text { but less than } 16 \text {. }$