Topic
Q:
Evaluate or simplify the expression without using a calculator.
\( e^{\ln 3 x^{3}} \)
\( e^{\ln 3 x^{3}}=\square \)
Q:
Evaluate or simplify the expression without using a calculator.
\( e^{\ln 146} \)
Q:
27 Multiple Choice 1 point
Solve the problem.
The population of an animal species in a certain area is modeled by \( \mathbf{F}(\mathrm{t})=400 \mathrm{log}(2 t+3) \) where \( t \) is the time in months since the species was introduced to the area. Find the
population of this species in the area 6 months after the species is introduced.
74
704
240
Q:
6. Graph \( y=\log _{\frac{1}{2}}(x)+ \) 2. Analyze the function where \( 0<b<1 \).
Domain:
Range:
\( \lim _{x \rightarrow 0^{+}} f(x) \)
Q:
Find the vertical and horizontal asymptotes for \( g(x)=\frac{\sqrt{x^{2}-4}}{2-x} \)
Q:
Hence, determine a general formula for the pattern \( 0 ;-6 ;-20 ;-42 \ldots \)
Simplify your answer as far as possible.
ESTION 4
c) \( =-2 x^{2}+2 \) and \( g(x)=2^{x}+1 \) are the defining equations of graphs \( f \) and \( g \) respectively.
Write down an equation for the asymptote of \( g \).
Sketch the graphs of \( f \) and \( g \) on the same set of axes, clearly showing ALL
intercepts with the axes, turning points and asymptotes.
Write down the range of \( f \).
Determine the maximum value of \( h \) if \( h(x)=3 /(x) \).
What transformation does the graph of \( y=f(x) \) undergo in order to obtain the
Q:
11
A ball is dropped from a height of 10 feet. The ball repeatedly bounces, and the maximum height of the ball
after each bounce is \( 20 \% \) less than the previous maximum height. Which of the following arguments is
correct regarding a sequence that can be used to model the successive maximum heights, in feet?
Q:
2 Encontrar el dominio de la función
\( A(x)=\frac{\sqrt{\frac{x}{x-1}}}{|x|-\left|\frac{3}{2} x+5\right|} \)
Q:
1. Transform the following equations to canonical forms
a) \( x^{2}+4 x y+4 y^{2}-20 x+10 y-50=0 \)
b) \( 3 x^{2}+10 x y+3 y^{2}-12 x-12 y+4=0 \)
c) \( x^{2}+2 x y+y^{2}-4 x-4 y+3=0 \)
d) \( 9 x^{2}+24 x y+16 y^{2}-126 x+82 y-59=0 \)
e) \( 3 x^{2}-8 x y-3 y^{2}+10 x-13 y+8=0 \)
f) \( 3 x^{2}-5 x y+6 y^{2}+11 x-17 y+13=0 \)
g) \( 9 x^{2}+24 x y+16 y^{2}+34 x+62 y+47=0 \)
h) \( x^{2}-4 x y+4 y^{2}-12 x-6 y-39=0 \)
Q:
Realice la gráfica de la siguiente función: \( g(x)=\log _{5}(x-6) \)
Luego indique:
a) Dominio y el rango de la función.
b) Ecuación de la asíntota.
c) Intercepto con los ejes.
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