Precálculo preguntas y respuestas

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 \( f(x) \).

Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.

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 \( y=f(x) \).

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.

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?

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?

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?

Graph \( m(w)=-2 \cdot 2^{w} \)

Find the equation for the exponential function that passes through the points \( (2,4) \) and \( (4,11) \).

Given two points for an exponential function, 1. Use the two points to find the growth rate, k . Write an exponential model for each point, then solve this system of two equations for k . 2. Use either point with the k you found to find the initial amount at time zero, \( \mathrm{A}_{\mathrm{o}} \). 3. Doubling time is when the amount is \( 2^{*} \mathrm{~A}_{\mathrm{o}} \). 4. Use the values of k and \( \mathrm{A}_{\mathrm{o}} \) to calculate the amount for a given time or to find the time to reach a specific amount in the future. The count in a bacteria culture was 600 after 20 minutes and 1900 after 30 minutes. Assuming the count grows exponentially. You may enter the exact value or round to 2 decimal places. What was the initial size of the culture? Find the doubling period. Find the population after 105 minutes. When will the population reach 14000 .