Tema
Q:
P. 3
Use the product rule to simplify the expressions in Exercises 41-44.
In Exercises \( 43-44 \), assume that variables represent nonnegative
real numbers.
\( \begin{array}{ll}\text { 41. } \sqrt{300} & \text { 42. } \sqrt{12 x^{2}} \\ \text { 43. } \sqrt{10 x} \cdot \sqrt{2 x} & \text { 44. } \sqrt{r^{3}}\end{array} \)
Q:
33.33 Points] DETAILS MY NOTES SPRECALC8 4.7.010.
(a) Find the magnitude of an earthquake that has an intensity that is 75.3 (that is, the amplitude of the seismograph reading is 75.3 cm ).
(Round your answer to one decimal place.)
Q:
\( y = x ^ { 2 } - 1 ; [ - 1,1 ] \)
Q:
8. The population of a community (in millions) can be approximated by
\( p(t)=38.3 e^{x \ln 1.024} \), where \( t \) is years after 2000 .
a. What is the estimated population for the year 2030 ?
78.018 Million of people
Q:
Calcular los valores que toman las funciones \( y=3^{x} \)
\( y y=2^{x} \), para \( x=-3,-2,-1,0,1 \) y 2 . Elaborar
una tabla de valores \( y \) representar sobre un mismo
plano cartesiano las dos funciones.
¿Qué tienen en común las gráficas de las funciones
\( y=2^{x} y y=3^{x} \) ?
Q:
Find the domain and range of \( y=f(x)=\frac{1}{\sqrt{4-x^{2}}} \)
Q:
Sketch the groph of the
following ratonal function
and stche heir property
a. \( f(x)=\frac{x^{3}-1}{x^{2}-3 x+2} \)
b. \( f(x)=\frac{x^{2}}{x^{2}+1} \)
Q:
QUESTION 7
Given: \( f(x)=\frac{2}{x+4}-1 \)
7.1 Write down the equation of the asymptotes of \( f \).
7.2 Calculate the intercepts of the graph of \( f \) with the axes.
7.3 Sketch the graph of \( f \), showing clearly the asymptotes and intercepts with the
axes.
7.4 Write down the coordinates of the image of the \( x \)-intercept if it is reflected about
the axis of symmetry \( y=-x-5 \).
7.5 Write down the range of \( y=-f(x) \).
Describe in words, the transformation of \( f \) to \( g \) if \( g(x)=\frac{-2}{x-4}-1 \).
Q:
5. Trazar las gráficas de las siguientes funciones, determinando dominio \( y \)
\( \begin{array}{llll}\text { a. } F(x)=x^{2}-2 x & \text { b. } F(x)=-x^{2}-2 x & \text { c. } F(x)=x^{2}-2 x+2 & \text { d. } f(x)=\sqrt{x^{2}-2 x} \\ \text { e. } f(x)=\sqrt{-x^{2}-2 x} & \text { f. } F(x)=\left|x^{2}-2 x\right| & \text { g. } F(x)=\left|-x^{2}-2 x\right|\end{array} \)
Q:
2. Tyler filled up his bathtub, took a bath, and then drained the tub. The function \( B \)
gives the depth of the water, in inches, \( t \) minutes after Tyler began to fill the bathtub.
Explain the meaning of each statement in this situation.
a. \( B(0)=0 \)
b. \( B(1)<B(7) \)
c. \( B(9)=11 \)
d. \( B(10)=B(22) \)
e. \( B(20)>B(40) \)
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