Answer Happy

1) Based on the function f(x)=x+42x−4​, state the following: {10} a) x-intercept(s) b) y-intercept c) Domain d) range e) vertical asymptote(s) f) horizontal asymptote g) positive interval h) negative interval i) intervals of increase j) intervals of decrease 2) Describe how the graph of y=−2f[3(x−1)]−4 can be obtained from the graph of f(x)=x4. Be sure to use full sentences when describing the transformations. {4} 3) The population of a small town is modelled by the function P(t)=2t+520(4t+3)​, where P(t) is the population, in thousands, and t is time, in years, since the start of 1990 . a) Is the population currently increasing or decreasing? Justify your answer. {2} b) The town will need its own transit system if the population exceeds 50000 . Will the town's population ever exceed 50000? Explain. {2} 4) Polluted water from a factory flows into a pond. The concentration of pollutant, c, in the pond at time t ​ minutes is modelled by the equation c(t)=8−8000(1000+2t1​), where c is measured in kg/m3. When will the concentration of pollutant in the pond reach 6 kg/m3 ? {4} 5) Solve x−52x−1​>x+5x+1​ {5}