Tema
Q:
\( f(t)=\frac{560}{1+5.2 e} \)-o.lle
Solve the problem. the equation
describes the population of a species of 1
butterflies \( t \) moaths after they
are introdveed to a non threntening habitat.
What is the limiting size of the
butterfly population that the habitat will substain?
Q:
The exporential model \( A=195.7 e^{0.027 t} \)
describes the population, \( A \), of a country
in millions, \( t \) years after 2003 . Use
the model to determine when the
population of the country will be 301 million
Q:
1. Halle el dominio de las siguientes funciones:
\( \begin{array}{lll}\text { a) } f(x)=\frac{1}{x-2} . & \text { b) } g(x)=\frac{x-1}{x^{2}-2} . & \text { c) } h(x)=\frac{\sqrt{x+3}}{x^{2}-2 x+1} \\ \text { 2. Hallar el dominio y rango de las siguientes funciones: } & \text { b) } f(x)=\ln (2 x+1) . & \text { c) } f(x)=e^{x^{2}}+1\end{array} \)
Q:
Analyze the graph of the function.
\( R(x)=\frac{3 x+3}{7 x+21} \)
(a) What is the domain of \( R(x) \) ?
A. \( \{x \mid x \neq 0 \) and \( x \neq-3\} \)
B. \( \{x \mid x \neq 0 \) and \( x \neq-3 \) and \( x \neq-1\} \)
C. \( \{x \mid x \neq-3\} \)
D. All real numbers
(b) What is the equation of the vertical asymptote(s) of \( R(x) \) ? Select the correct choice below and fill in any answer boxes within your choice.
A. \( x=\square \)
(Use a comma to separate answers as needed. Type an integer or a fraction.)
Q:
Parmi les énoncés suivants, lesquelles sont vrais ?
Sélectionnez un ou plusieurs choix.
\( 10^{x} \) est proportionnel à \( e^{x} \)
Le logarithme de \( 2,5 * x^{1,3} \) est proportionnel au logarithme de \( x \)
Le logarithme de \( 6,7 * x^{-0,1} \) est une fonction affine du logarithme de \( x \)
Q:
Cara is about to ride the fastest roller coaster in the world. The function \( f(x) \) gives
the speed of the roller coaster in miles per hour \( x \) seconds after the ride starts.
What does \( f(25)>123 \) tell you?
The roller coaster is moving faster than 25 miles
per hour 123 seconds after the ride starts.
The roller coaster is moving faster than 123 miles
per hour 25 seconds after the ride starts.
Q:
Analyze the graph of the function.
\( R(x)=\frac{x+4}{x(x+8)} \)
(a) What is the domain of \( R(x) \) ?
A. \( \{x \mid x \neq 0 \) and \( x \neq-8 \) and \( x \neq-4\} \)
B. \( \{x \mid x \neq 0 \) and \( x \neq-4\} \)
C. \( \{x \mid x \neq 0 \) and \( x \neq-8\} \)
D. All real numbers
(b) What is the equation of the vertical asymptote(s) of \( R(x) \) ? Select the correct choice below and fill in any answer boxes within your choice.
A. \( x=\square \)
(Use a comma to separate answers as needed. Type an integer or a fraction.)
Q:
4) \( f(x)=\left\{\begin{array}{lr}0 & -2<x<-1 \\ -2 & -1 \leq x<0 \\ 1 & 0 \leq x<1 \\ 0 & 1 \leq x<2\end{array}\right. \)
Q:
Identify any horizontal and vertical asymptotes and any holes in the graph. \( f(x)=\frac{x^{2}+2 x+1}{x+1} \)
End Behavior:
There is a horizontal asymptote at
There is no horizontal asymptote
Vertical Asymptote
There is a vertical asymptote at
Q:
Find the domain of the function.
\[ g(x)=\ln (x+8) \]
The domain of \( g \) is
(Type your answer in interval notation.)
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