4 1 Inverse Functions 1 Determine if each pair of functions is an inverse function a 2 5 2 10 b 2 1 1 c 3 2 3 3 3 1 2 Given that what is the domain of 1 1 1 4 5 3 Find for original functions Identify the domain and range of both the inverse and 4 Given each function show your work to find the inverse Identify the domain and range of the function and its inverse Then graph both Clearly label both functions on the graph a 2 3 2 1 b x 1 c 4 4 2 Exponential Functions 1 A colony of bees starts with 1000 bees and grows at a rate of 5 per year a Write an equation to model the bee population P as a function of time t b What is the number of bees after 5 years 2 Lawrence in 2023 had a population of 96 000 The population grows at a rate of 0 65 per year a Write an equation to model the population P as a function of time t b What is the population going to be in 2030 3 After I left Topeka the population has been decreasing 10 each year The population of Topeka was 125 000 in 2023 a Write an equation to model the population P as a function of time t b What is the population going to be in 203387 4 You deposit 1 000 into a savings account The annual interest rate is 5 Which investment yields the greater return over 2 years the interest rate compounded quarterly or the interest rate compounded continuously How much more is yielded by the better investment to the nearest cent 4 3 Exponential Logarithmic Functions Graphs 1 Use transformations to make accurate graphs of each function Find the domain and range of each function Find the equation of the asymptote of each function a 2 b c 3 2 d 3 2 e 2 2 f 1 4