Exam 2: Limits and the Derivative

For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). -

For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). -

Use the properties of logarithms to solve. -

Sketch the graph of the function. -

Use the REGRESSION feature on a graphing calculator. -The total cost of the Democratic and the Republican national conventions has increased 596% over the 20-year period between 1980 and 2004. The following table lists the total cost, in millions of dollars, for selected years. Find the exponential functions that best estimates this data. Round your answer to four decimal places

Find the x-intercept(s) if they exist. -

Use the REGRESSION feature on a graphing calculator. -A particular bacterium is found to have a doubling time of 20 minutes. If a laboratory culture begins with a population of 300 of this bacteria and there is no change in the growth rate, how many bacteria will be present in 55 minutes? Use six decimal places in the interim calculation for the growth rate.

Write an equation for a function that has a graph with the given transformations. -The shape of is shifted 5 units to the left. Then the graph is shifted 7 units upward.

Solve the problem. -The following table shows a recent state income tax schedule for married couples filing a joint return in State X. (i) Write a piecewise definition for the tax due T(x) on an income of x dollars. (ii) Graph T(x). (iii) Find the tax due on a taxable income of $50,000. Of $95,000.

Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. -

Provide an appropriate response. -Graph f(x) = and indicate the maximum or minimum value of f(x), whichever exists.

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y. -y = x

Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. -

For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y. -

Graph the function. -

Solve the problem. -The level of a sound in decibels (db) is determined by the formula he formula ) db, where I db, where Iis the intensity of the sound in watts per square meter. A certain noise has an intensity of 8.49 × 10-4 watts per square Meter. What is the sound level of this noise? (Round your answer to the nearest decibel.)

Determine if the equation specifies a function with independent variable x. If so, find the domain. If not, find a value of x to which there corresponds more than one value of y. -xy = -7

For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. -

Determine the domain of the function. -f(x) = - 7x + 9