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Q:
Question 7 (1 point)
Compared to the graph of the function \( f(x)=\frac{1}{x} \), the graph of the function \( g(x)=\frac{1}{x-1} \) is
translated
A) 1 unit up
B) 1 unit to the right
C) 1 unit down
D) 1 unit to the left
Q:
(1) EJercitación. Trazar la gráfica de cada funcion. Determinar su dominio y su rango
es creciente, decreciente y constante.
\( \begin{array}{ll}\text { 1. } f(x)=\left\{\begin{array}{ll}x+1 & \text { si } x>0 \\ -2 x-3 & \text { si } x \leq 0\end{array}\right. \\ \text { 4. } f(x)=\left\{\begin{array}{ll}x+2 & \text { si } x<-1 \\ x+4 & \text { si } x>-1 \\ x^{2} & \text { si } x>1 \\ x^{3} & \text { si } x \leq 1\end{array}\right. \\ \begin{array}{ll}x+2 & \text { si } x=-1\end{array} & \text { 5. } f(x)=\left\{\begin{array}{ll}(x-1)^{2} & \text { si } x>2 \\ x+2 & \text { si } x \leq 2\end{array}\right.\end{array} \)
Q:
(4 of 10)
The graph \( f(x) \) is transformed by the following sequence.
1. Shift right 5 units
2. Reflect over \( y \)-axis
3. Shift down 8 units
\( \begin{array}{l}y=-f(x-5)-8 \\ y=-f(x+5)-8 \\ y=f(-x+5)-8 \\ \text { Which is an equation for the new graph? } \\ \begin{array}{l}y \\ y\end{array}\end{array} \)
Q:
HALLAR EL DOMINIO DE \( F(x)=\sqrt{L N(x-S)} \)
Q:
13. Dada la función \( f(x)=\log _{2} x \)
Sin utilizar tablas de valores dibuja las
funciones:
\( g(x)=3+\log _{2} x \)
\( h(x)=-1+\log _{2} x \)
\( m(x)=\log _{2}(x+2) \)
\( f(x)=\log _{2}(x-4) \)
Q:
\( i + i ^ { 2 } + i ^ { 3 } + \ldots + i ^ { 2023 } \)
Q:
Given the function \( f(x)=3 x^{2}+5, x \geq 0 \), determine if \( f(x) \) is one-to-one. If it is, find a formula for the inverse.
Is \( f(x) \) one-to-one?
No
\( f^{-1}(x)=\square \)
Yes
Type an exact answer, using radicals as needed.)
Q:
Use the graph of \( f(x) \) to determine whether the function is one-to-one. If it is, find a formula for its inverse.
\( f(x)=\frac{x+7}{x-5} \)
Is the function one-to-one?
No 2
Yes
Q:
Question 5
The population of a rural county is decreasing. The population in 2014 was 230,000 and the population in
2021 was 212,000 . Assuming that decay is exponential (with natural base \( e \) ), what is the yearly decay
rate? State answer as a percentage rounded to one decimal place.
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Q:
La ecuación cartesiana \( \left(x^{2}+y^{2}\right)^{2}=2\left(x^{2}-\right. \)
\( \left.y^{2}\right) \) en coordenadas polares
corresponde a:
\( \begin{array}{l}r^{2}=2 \cos 2 \theta \\ r=6 \cos 2 \theta \\ r^{2}=6 \cos 2 \theta \\ \end{array} \)
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