Exam 2: Limits and the Derivative

Solve the problem. -The function F described by F(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose Humerus is 30.93 cm long. Round your answer to the nearest four decimal places.

Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -

Provide an appropriate response. -Only one of the following functions has domain which is not equal to all real numbers. State which function and state its domain. (A) h(x) (B)

Solve the problem. -Since life expectancy has increased in the last century, the number of Alzheimer's patients has increased dramatically. The number of patients in the United States reached 4 million in 2000. Using data collected since 2000, it has been found that the data can be modeled by the exponential function l function where X is the years since 2000. Estimate the Alzheimer's patients in 2025. Round to the nearest tenth.

Evaluate. -

Find the equation of any horizontal asymptote. -

Determine whether the relation represents a function. If it is a function, state the domain and range. -{(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)}

Solve the problem. -A retail chain sells washing machines. The retail price p(x) (in dollars) and the weekly demand x for a particular model are related by the function . (i) Describe how the graph of the Function p can be obtained from the graph of one of the six basic functions: y or y = x . (ii) Sketch a graph of function p using part (i) as an aid.

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. -

Find the vertex form for the quadratic function. Then find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -

Solve the problem. -The U. S. Census Bureau compiles data on population. The population (in thousands) of a southern city can be approximated by P(x) 927, where x c where x or responds to the years after 1950. In what calendar Year was the population about 804,200?

Find the equations of any vertical asymptotes. -

Graph the function. -Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Graph y = L(x). Use the Interval (0, 4].

For the following problem, (i) graph f and g in the same coordinate system; (ii) solve f(x) = g(x) algebraically to two decimal places; (iii) solve f(x) > g(x) using parts i and ii; (iv) solve f(x) < g(x) using parts i and ii. -

Use the properties of logarithms to solve. -

Provide an appropriate response. -How can the graph of be obtained from be obtained from the graph of

Find the function value. -Find f(-9) when ) when f(x

Provide an appropriate response. -What is the maximum number of x intercepts that a polynomial of degree 10 can have?

Solve the problem. -In the table below, the amount of the U.S. minimum wage is listed for selected years. Find an exponential regression model of the form he form y , where y, where y represents the U.S. minimum wage x years after 1960. Round a and b to four decimal places. According to this model, what will the minimum wage be in 2005? In 2010?

Find the equation of any horizontal asymptote. -