Tema
Q:
Let \( P=(x, y) \) be a point on the graph of \( y=x^{2}-2 \). Complete parts (a) through (e) below.
(a) Express the distance \( d \) from \( P \) to the origin as a function of \( x \).
\( d(x)= \)
(Simplify your answer. Type an exact answer, using radicals as needed.)
Q:
Given \( f(x)=\frac{-2}{x}-2 \), Answer the following questions:
.1 Write down the equations of the asymptotes of \( f(x) \).
2 Draw a neat sketch graph of \( f(x) \), clearly indicate the asymptotes
and the intercepts with the axes.
.3 Write down the domain and range of \( f(x) \).
Q:
Given: \( f(x)=2\left(x^{2}-1\right) \)
Sketch function \( f \) on the diagram sheet.
Clearly show all intercepts with the axes.
Q:
Complete the sentence below.
Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about
the -axis of the graph of the function \( y=f(x) \).
Suppose that the graph of a function \( f \) is known. Then the graph of \( y=f(-x) \) may be obtained by a reflection about
the -axis of the graph of the function \( y=f(x) \).
Q:
QUESTION 4
Given: \( f(x)=2\left(x^{2}-1\right) \)
Sketch function \( f \) on the diagram sheet.
Clearly show all intercepts with the axes.
Q:
The logistic growth function \( f(t)=\frac{111,000}{1+5400 e^{-t}} \) describes
the number of people, \( f(t) \), who have become ill
with influenza \( t \) weaks wfter its inital outbreak
in a puticular community.
a) How may people became ill with the flu
when the epidemic began?
b) How many people were ill by the end of
the fourth week?
c) what is the limiting size of the population
that become ill?
Q:
The exponential model \( A=177.2 e^{0.013 t} \)
describe the population, \( A_{1} \) of a country
in millions, \( t \) years after 2003 . Use the
model to answer the following questions:
a) what was the population of the
country in 2003 ?
b) By what percentage is the papulation
of the country increasing each year?
Q:
2. (2.5 pts) Demuestra que para todo número natural \( n \),
\[ 1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n+1}} \geq \sqrt{n+1} \]
¿A partir de qué número \( n \) se empieza a cumplir la desigualdad estricta
\( > \), sin el igual?
Q:
Graph \( m(w)=-2 \cdot 2^{w} \)
Q:
Find the equation for the exponential function
that passes through the points \( (2,4) \) and \( (4,11) \).
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