Math 131 Exam 1Review 1 A line contains the point 2 6 On this line each increase of 3 in x produces a decrease of 9 in y Find the y intercept of this line 2 Write the function that is the result of y e x after applying the following transformations in the given order reflection across the y axis shift left 2 units stretch vertically by a factor of 4 3 The half life of a drug in the body is 4 days What portion of the original amount taken is present after 12 days 4 A substance weighed 20g at time t 0 days It grew exponentially so that at t 6 days it weighed 30g At how many days will it weigh 50g Round the number of days to 2 decimal places if needed sin 5x x 0 3x 5 Use your calculator to evaluate lim 6 Find lim 2 ln x 3 x 3 4 x 2 Ax x 3 7 f x 2x A 3 x Find the value of A that makes f x continuous for all x 8 f x 5 2 x 6 Find f 1 34 9 f x ln a b x can be simplified to what type of function Write its equation 10 For f x ln x 2 1 and g x e x h x g f x simplifies to what function 11 For the data points x 1 2 3 4 5 y 2 5 3 5 8 Find the cubic regression model Write the leading coefficient rounded to 3 decimal places if necessary What does the cubic model predict for the y value when x 6 Viewing the graph which two data points are closest to the cubic regression model 12 A substance initially weighed 25 g but decays exponentially After six years it weighs 20 g a What will it weigh after 12 years b Write the equation for the weight in grams after t years c Find the half life of the substance rounded to three decimal places if necessary 13 Evaluate each limit as a number as or state DNE For a and b f x a d lim f x x 3 lim x 0 tan x x x2 x 6 x 2 5x 6 1 x b lim f x c lim tan Use the calculator Keep zooming in x 2 x 0 Use the calculator 14 2 x ln 2 x x 2 7 x 10 2 x 7 x 5 f x x 2 4 x 5 3x 7 x or x 5 Evaluate each of the following lim f x x 2 lim f x x 2 f 2 Is f continuous at x 2 What is seen in the graph at x 2 lim f x lim f x f 5 x 5 x 5 Is f continuous at x 5 lim f x x 7 lim f x x 7 Is f continuous at x 7 What is seen in the graph at x 5 f 7 What is seen in the graph at x 7 15 Find the least squares regression line for the points The y value on this line when x 1 5 is 16 1 7 2 11 and 3 12 y A e 3 x If x increases by 2 then what is the change in ln y 17 A culture grows so that its weight is doubled every 4 days In how many days will the weight triple 18 Find the inverse function to f x 3 e x 1 f 8 3 and f x is an even function what other point must be on f x 19 Given that the graph of sin 0 5 and sin x is an odd function what other point must be 6 on the graph of sin x 20 a Given that b Use part a and f x sin x on on the inverse function 21 Find the inverse function to f x is one to one What two points must be 2 2 3x 2 Find the domain of each function x 5 Find the range of each function f x 3 x 2 4 x 9 f x h f x a Evaluate and simplify it h 22 For f x h f x h 23 Find all solutions to 2 log3 x 2 log3 x 4 2 b Find lim h 0 24 Find the domain of the function f x ln x 2 9 x 1 f x x 2 25 x 2 2 x a Find the average rate of change of b Find the average rate of change of 26 Find a 27 3e x 5 lim x x 2e 6 3x 2 4 lim x 5 x 2 f x for x 0 to x 2 f x for x 3 to x 6 3e x 5 b lim x 2e x 6