Pre Calculus Questions & Answers

Graph the logarithmic function \( g(x)=-\log _{3} x-1 \). To do this, plot two points on the graph of the function, and also draw the asymptote. Additionally, give the domain and range of the function using interval notation.

Graph the logarithmic function \( g(x)=\log _{3}(x-1)-2 \). To do this, plot two points on the graph of the function, and also draw the asymptote. \( T \) Additionally, give the domain and range of the function using interval notation.

Graph the exponential function \( g(x)=\left(\frac{1}{3}\right)^{x}-1 \). To do this, plot two points on the graph of the function, and also draw the asymptote. Additionally, give the domain and range of the function using interval notation.

Graph the exponential function \( g(x)=-\left(\frac{1}{4}\right)^{x}+2 \). To do this, plot two points on the graph of the function, and also draw the asymptote. Additionally, give the domain and range of the function using interval notation.

Graph the exponential function \( g(x)=-\left(\frac{1}{4}\right)^{x}+2 \). To do this, plot two points on the graph of the function

Graph the exponential function \( g(x)=2^{x+1} \). To do this, plot two points on the graph of the function, and also draw the asymptote. Then click on the graph-a-function button. Additionally, give the domain and range of the function using interval notation.

Mitchell is an ecologist studying bonobos, a species of ape that lives in the Congolian rainforest. When he started his study, there was a population of about 40,000 bonobos. After one year, he estimated that the population had decreased to 39,200 . Based on his data, Mitchell expects the population to continue decreasing each year. Write an exponential equation in the form \( y=a(b)^{x} \) that cal model the bonobo population, \( y, x \) years after Mitchell began studying them. Use whole numbers, decimals, or simplified fractions for the values of a and \( b \). \( y=\square \) To the nearest hundred, what can Mitchell expect the bonobo population to be 7 years after the study began? bonobos

Find the domain of the function. \[ f(x)=\ln \left(9-x^{2}\right) \] Write your answer as an interval or union of intervals.

5) Find the equation of the exponential function that goes through \( \left(-1, \frac{2}{5}\right) \) and \( (2,50) .(4 \) pts)

Below is the graph of \( y=\left(\frac{1}{2}\right)^{x} \). Translate it to become the graph of \( y=\left(\frac{1}{2}\right)^{x+1}-4 \).